In this chapter G = (V,E) denotes an arbitrary undirected graph without loops, where V = {v 1, v 2,…, v n } is its vertex set and E = {e 1,e 2,…, e m } ⊂ (E ×E) is its edge set. Two edges are adjacent if they connect to a common vertex. Two vertices v i and v j are adjacent if there is an edge e = (v i ,v j ) ∈ E. Finally, if e = (v i ,v j ) ∈ E,we say e is incident to vertices v i , v j .

The Graph Coloring Problem: A Bibliographic Survey

In this paper, two new concepts-Coloring-Contradiction (CC) and Non-Coloring-Contradiction Graph (NCCG) are introduced and some of their main properties are studied. The counting problem of NCCG is discussed, and a simple and efficient modification of the algorithm for coloring a graph is also presented.

The graphs of non-coloring-contradiction and the algorithm for coloring a graph

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The graphs of non-coloring-contradiction and the algorithm for coloring a graph