منابع مشابه
Online coloring graphs with high girth and high odd girth
We give an upper bound for the online chromatic number of graphs with high girth and for graphs with high oddgirth generalizing Kierstead’s algorithm for graphs that contain neither a C3 or C5 as an induced subgraph. keywords: online algorithms, combinatorial problems
متن کاملEquitable coloring planar graphs with large girth
A proper vertex coloring of a graph G is equitable if the size of color classes differ by at most one. The equitable chromatic threshold of G, denoted by ∗Eq(G), is the smallest integer m such that G is equitably n-colorable for all n m. We prove that ∗Eq(G) = (G) if G is a non-bipartite planar graph with girth 26 and (G) 2 or G is a 2-connected outerplanar graph with girth 4. © 2007 Elsevier B...
متن کاملStar Coloring High Girth Planar Graphs
A star coloring of a graph is a proper coloring such that no path on four vertices is 2-colored. We prove that every planar graph with girth at least 9 can be star colored using 5 colors, and that every planar graph with girth at least 14 can be star colored using 4 colors; the figure 4 is best possible. We give an example of a girth 7 planar graph that requires 5 colors to star color.
متن کامل(2 + ϵ)-Coloring of planar graphs with large odd-girth
The odd-girth of a graph is the length of a shortest odd circuit. A conjecture by Pavol Hell about circular coloring is solved in this article by showing that there is a function f( ) for each : 0 < < 1 such that, if the odd-girth of a planar graph G is at least f( ), then G is (2 + )-colorable. Note that the function f( ) is independent of the graph G and → 0 if and only if f( )→∞. A key lemma...
متن کاملColoring squares of planar graphs with girth six
Wang and Lih conjectured that for every g ≥ 5, there exists a number M(g) such that the square of a planar graph G of girth at least g and maximum degree ∆ ≥ M(g) is (∆+1)-colorable. The conjecture is known to be true for g ≥ 7 but false for g ∈ {5, 6}. We show that the conjecture for g = 6 is off by just one, i.e., the square of a planar graph G of girth at least six and sufficiently large max...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2016
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-016-1361-2