2-distance coloring of not-so-sparse graphs
نویسنده
چکیده
The square G of a graph G is the graph obtained from G by adding an edge between every pair of vertices having a common neighbor. A proper coloring of G is also called a 2-distance coloring of G. The maximum average degree Mad(G) of a graph G is the maximum among the average degrees of the subgraphs of G, i.e. Mad(G) = max { 2|E(H)| V (H) |H ⊆ G } . Graphs with bounded maximum average degree are often called sparse graphs. There are results about the chromatic number of G with Mad(G) < m for several values of m, all striclty lesser than 4. We provides upper and lower bounds for the chromatic number of G when Mad(G) < 2k for every k ≥ 2, and conjecture that our lower bounds are best possible.
منابع مشابه
2-distance Coloring of Sparse Graphs
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