Identifier
Mp00046: Ordered trees —to graph⟶ Graphs
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00172: Integer compositions —rotate back to front⟶ Integer compositions
Images
=>
Cc0021;cc-rep-0Cc0020;cc-rep-1
[]=>([],1)=>[1]=>[1] [[]]=>([(0,1)],2)=>[1,1]=>[1,1] [[],[]]=>([(0,2),(1,2)],3)=>[2,1]=>[1,2] [[[]]]=>([(0,2),(1,2)],3)=>[2,1]=>[1,2] [[],[],[]]=>([(0,3),(1,3),(2,3)],4)=>[3,1]=>[1,3] [[],[[]]]=>([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2] [[[]],[]]=>([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2] [[[],[]]]=>([(0,3),(1,3),(2,3)],4)=>[3,1]=>[1,3] [[[[]]]]=>([(0,3),(1,2),(2,3)],4)=>[2,2]=>[2,2] [[],[],[],[]]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]=>[1,4] [[],[],[[]]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[2,3] [[],[[]],[]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[2,3] [[],[[],[]]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[2,3] [[],[[[]]]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[2,3] [[[]],[],[]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[2,3] [[[]],[[]]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[2,3] [[[],[]],[]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[2,3] [[[[]]],[]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[2,3] [[[],[],[]]]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]=>[1,4] [[[],[[]]]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[2,3] [[[[]],[]]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[2,3] [[[[],[]]]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]=>[2,3] [[[[[]]]]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[3,2]=>[2,3] [[],[],[],[],[]]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]=>[1,5] [[],[],[],[[]]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[],[],[[]],[]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[],[],[[],[]]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[],[],[[[]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[],[[]],[],[]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[],[[]],[[]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[],[[],[]],[]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[],[[[]]],[]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[],[[],[],[]]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[],[[],[[]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[],[[[]],[]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[],[[[],[]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[],[[[[]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[]],[],[],[]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[]],[],[[]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[]],[[]],[]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[]],[[],[]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[]],[[[]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[],[]],[],[]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[[]]],[],[]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[],[]],[[]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[[]]],[[]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[],[],[]],[]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[],[[]]],[]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[[]],[]],[]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[[],[]]],[]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[[[]]]],[]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[[],[],[],[]]]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]=>[1,5] [[[],[],[[]]]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[],[[]],[]]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[],[[],[]]]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[],[[[]]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[[]],[],[]]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[[]],[[]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[[],[]],[]]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[[[]]],[]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[[],[],[]]]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[[],[[]]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[[[]],[]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[3,3]=>[3,3] [[[[[],[]]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[4,2]=>[2,4] [[[[[[]]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[3,3]=>[3,3] [[],[],[],[],[],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1,6] [[],[],[],[],[[]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[],[],[],[[]],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[],[],[],[[],[]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[],[],[],[[[]]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[],[],[[]],[],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[],[],[[]],[[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[],[],[[],[]],[]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[],[],[[[]]],[]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[],[],[[],[],[]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[],[],[[],[[]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[],[],[[[]],[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[],[],[[[],[]]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[2,5] [[],[],[[[[]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[3,4] [[],[[]],[],[],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[],[[]],[],[[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[],[[]],[[]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[],[[]],[[],[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[],[[]],[[[]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[],[[],[]],[],[]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[],[[[]]],[],[]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[],[[],[]],[[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[],[[[]]],[[]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[],[[],[],[]],[]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[],[[],[[]]],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[],[[[]],[]],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[],[[[],[]]],[]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[2,5] [[],[[[[]]]],[]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[3,4] [[],[[],[],[],[]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[],[[],[],[[]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[],[[],[[]],[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[],[[],[[],[]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[],[[],[[[]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[],[[[]],[],[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[],[[[]],[[]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[],[[[],[]],[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[],[[[[]]],[]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[],[[[],[],[]]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[],[[[],[[]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[],[[[[]],[]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[],[[[[],[]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[3,4] [[],[[[[[]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[3,4] [[[]],[],[],[],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[]],[],[],[[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[]],[],[[]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[]],[],[[],[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[]],[],[[[]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[]],[[]],[],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[]],[[]],[[]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[]],[[],[]],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[]],[[[]]],[]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[]],[[],[],[]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[]],[[],[[]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[]],[[[]],[]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[]],[[[],[]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[3,4] [[[]],[[[[]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[3,4] [[[],[]],[],[],[]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[[]]],[],[],[]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[],[]],[],[[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[]]],[],[[]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[],[]],[[]],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[]]],[[]],[]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[],[]],[[],[]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[2,5] [[[],[]],[[[]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[3,4] [[[[]]],[[],[]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[3,4] [[[[]]],[[[]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[3,4] [[[],[],[]],[],[]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[],[[]]],[],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[]],[]],[],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[],[]]],[],[]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[2,5] [[[[[]]]],[],[]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[3,4] [[[],[],[]],[[]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[],[[]]],[[]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[[]],[]],[[]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[[],[]]],[[]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[3,4] [[[[[]]]],[[]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[3,4] [[[],[],[],[]],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[],[],[[]]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[],[[]],[]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[],[[],[]]],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[],[[[]]]],[]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[[]],[],[]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[]],[[]]],[]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[],[]],[]],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[[]]],[]],[]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[[],[],[]]],[]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[[],[[]]]],[]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[[[]],[]]],[]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[[[],[]]]],[]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[3,4] [[[[[[]]]]],[]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[3,4] [[[],[],[],[],[]]]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1,6] [[[],[],[],[[]]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[],[],[[]],[]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[],[],[[],[]]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[],[],[[[]]]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[],[[]],[],[]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[],[[]],[[]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[],[[],[]],[]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[],[[[]]],[]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[],[[],[],[]]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[],[[],[[]]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[],[[[]],[]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[],[[[],[]]]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[2,5] [[[],[[[[]]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[3,4] [[[[]],[],[],[]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[[]],[],[[]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[]],[[]],[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[]],[[],[]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[]],[[[]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[[],[]],[],[]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[[[]]],[],[]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[[],[]],[[]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[[]]],[[]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[[],[],[]],[]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[[],[[]]],[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[[]],[]],[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[[],[]]],[]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[5,2]=>[2,5] [[[[[[]]]],[]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[3,4] [[[[],[],[],[]]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[[],[],[[]]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[],[[]],[]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[],[[],[]]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[],[[[]]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[[[]],[],[]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[[]],[[]]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[[],[]],[]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[4,3]=>[3,4] [[[[[[]]],[]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[[[],[],[]]]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[5,2]=>[2,5] [[[[[],[[]]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[[[[]],[]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[4,3]=>[3,4] [[[[[[],[]]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[4,3]=>[3,4] [[[[[[[]]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[4,3]=>[3,4]
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges.
Map
chromatic difference sequence
Description
The chromatic difference sequence of a graph.
Let $G$ be a simple graph with chromatic number $\kappa$. Let $\alpha_m$ be the maximum number of vertices in a $m$-colorable subgraph of $G$. Set $\delta_m=\alpha_m-\alpha_{m-1}$. The sequence $\delta_1,\delta_2,\dots\delta_\kappa$ is the chromatic difference sequence of $G$.
All entries of the chromatic difference sequence are positive: $\alpha_m > \alpha_{m-1}$ for $m < \kappa$, because we can assign any uncolored vertex of a partial coloring with $m-1$ colors the color $m$. Therefore, the chromatic difference sequence is a composition of the number of vertices of $G$ into $\kappa$ parts.
Map
rotate back to front
Description
The back to front rotation of an integer composition.