3 research outputs found

    Degenerate and star colorings of graphs on surfaces

    Get PDF
    AbstractWe study the degenerate, the star and the degenerate star chromatic numbers and their relation to the genus of graphs. As a tool we prove the following strengthening of a result of Fertin et al. (2004) [8]: If G is a graph of maximum degree Δ, then G admits a degenerate star coloring using O(Δ3/2) colors. We use this result to prove that every graph of genus g admits a degenerate star coloring with O(g3/5) colors. It is also shown that these results are sharp up to a logarithmic factor

    3-degenerate induced subgraph of a planar graph

    Full text link
    A graph GG is dd-degenerate if every non-null subgraph of GG has a vertex of degree at most dd. We prove that every nn-vertex planar graph has a 33-degenerate induced subgraph of order at least 3n/43n/4.Comment: 28 page
    corecore