Description

The chromatic number $\chi(G)$ of a graph $G=(V,E)$ is the minimum

number of colors needed to color $V(G)$ such that no adjacent vertices

receive the same color. The coloring number $\col(G)$ of

The chromatic number $\chi(G)$ of a graph $G=(V,E)$ is the minimum

number of colors needed to color $V(G)$ such that no adjacent vertices

receive the same color. The coloring number $\col(G)$ of a graph

$G$ is the minimum number $k$ such that there exists a linear ordering

of $V(G)$ for which each vertex has at most $k-1$ backward neighbors.

It is well known that the coloring number is an upper bound for the

chromatic number. The weak $r$-coloring number $\wcol_{r}(G)$ is

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Date Created
  • 2020
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    • Doctoral Dissertation Mathematics 2020

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