Identifier
Values
0 => ([(0,1)],2) => ([],2) => 1
1 => ([(0,1)],2) => ([],2) => 1
00 => ([(0,2),(2,1)],3) => ([],3) => 1
01 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 2
10 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 2
11 => ([(0,2),(2,1)],3) => ([],3) => 1
000 => ([(0,3),(2,1),(3,2)],4) => ([],4) => 1
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 3
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 2
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 3
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 3
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 2
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 3
111 => ([(0,3),(2,1),(3,2)],4) => ([],4) => 1
0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 1
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 1
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 1
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Description
The 2-dynamic chromatic number of a graph.
A $k$-dynamic coloring of a graph $G$ is a proper coloring of $G$ in such a way that each vertex $v$ sees at least $\min\{d(v), k\}$ colors in its neighborhood. The $k$-dynamic chromatic number of a graph is the smallest number of colors needed to find an $k$-dynamic coloring.
This statistic records the $2$-dynamic chromatic number of a graph.
Map
incomparability graph
Description
The incomparability graph of a poset.
Map
poset of factors
Description
The poset of factors of a binary word.
This is the partial order on the set of distinct factors of a binary word, such that $u < v$ if and only if $u$ is a factor of $v$.