We consider classes SCOLOR ( k ) of strongly k-colorable graphs and show that the recognition problem of SCOLOR ( k ) is NP-complete for every k ⩾ 4 , but it is ...
We give a characterization of SCOLOR ( 3 ) in terms of forbidden induced subgraphs. Finally, we solve the problem of uniqueness of a strong 3-coloring.
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List-coloring the square of a subcubic graph. The square G2 of a graph G is the graph with the same vertex set G and with two vertices adjacent if their ...
In 2006, a new coloring class has been proposed by Zverovich [7] . It includes a dominance relation between color classes and graph vertices. ... ... It is ...
Oct 21, 2016 · Without girth restriction, there exist planar graphs of fractional chromatic number exactly 4; describing planar graphs with smaller fractional ...
Sep 20, 2017 · New edge coloring problem in graph theory · 1 · Edges of every simple graph can be colored with at most s+1 color · 11 · Graphs with only ...
In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring ...
Jun 1, 2023 · The Four Color Theorem states that any planar graph can be colored using at most four colors, ensuring that no two adjacent vertices have the ...
A graph G is 2-colorable if and only if it is bipartite, and a bipartition is very nearly the same thing as a proper 2-coloring: just color vertices by which.
We discovered a new form of vertex colors of graphs (inherited directly form edge-colorings of perfect matchings) in the study of quantum physics questions.