- FindStat

Identifier

Mp00154: Graphs —core⟶ Graphs
St001110: Graphs ⟶ ℤ

Values

([],1) => ([],1) => 1

([],2) => ([],1) => 1

([(0,1)],2) => ([(0,1)],2) => 2

([],3) => ([],1) => 1

([(1,2)],3) => ([(0,1)],2) => 2

([(0,2),(1,2)],3) => ([(0,1)],2) => 2

([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3

([],4) => ([],1) => 1

([(2,3)],4) => ([(0,1)],2) => 2

([(1,3),(2,3)],4) => ([(0,1)],2) => 2

([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2

([(0,3),(1,2)],4) => ([(0,1)],2) => 2

([(0,3),(1,2),(2,3)],4) => ([(0,1)],2) => 2

([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2

([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

([],5) => ([],1) => 1

([(3,4)],5) => ([(0,1)],2) => 2

([(2,4),(3,4)],5) => ([(0,1)],2) => 2

([(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2

([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2

([(1,4),(2,3)],5) => ([(0,1)],2) => 2

([(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => 2

([(0,1),(2,4),(3,4)],5) => ([(0,1)],2) => 2

([(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => 2

([(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3

([(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,1)],2) => 2

([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,1)],2) => 2

([(0,1),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 5

([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3

([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

([],6) => ([],1) => 1

([(4,5)],6) => ([(0,1)],2) => 2

([(3,5),(4,5)],6) => ([(0,1)],2) => 2

([(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2

([(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2

([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2

([(2,5),(3,4)],6) => ([(0,1)],2) => 2

([(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 2

([(1,2),(3,5),(4,5)],6) => ([(0,1)],2) => 2

([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 2

([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2

([(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 2

([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2

([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,1)],2) => 2

([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => 2

([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,1)],2) => 2

([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,1)],2) => 2

([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => 2

([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,5),(1,4),(2,3)],6) => ([(0,1)],2) => 2

([(1,5),(2,4),(3,4),(3,5)],6) => ([(0,1)],2) => 2

([(0,1),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => 2

([(1,2),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1)],2) => 2

([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 5

([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => 2

([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3

([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 5

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Description

The 3-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 $3$-dynamic chromatic number of a graph.

Map

core

Description

The core of a graph.
The core of a graph $G$ is the smallest graph $C$ such that there is a homomorphism from $G$ to $C$ and a homomorphism from $C$ to $G$.
Note that the core of a graph is not necessarily connected, see [2].