Local chromatic number of quadrangulations of surfaces
نویسندگان
چکیده
منابع مشابه
Local chromatic number of quadrangulations of surfaces
The local chromatic number of a graph G, as introduced in [4], is the minimum integer k such that G admits a proper coloring (with an arbitrary number of colors) in which the neighborhood of each vertex uses less than k colors. In [17] a connection of the local chromatic number to topological properties of (a box complex of) the graph was established and in [18] it was shown that a topological ...
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A well-known result (Heawood [6], Ringel [11], Ringel and Youngs [10]) states that the maximum chromatic number of a graph embedded in a given surface S coincides with the size of the largest clique that can be embedded in S, and that this number can be expressed as a simple formula in the Eulerian genus of S. We study maximum chromatic number of k edge-disjoint graphs embedded in a surface. We...
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A method is suggested for construction of quadrangulations of the closed orientable surface with given genus g and either (1) with given chromatic number or (2) with given order allowed by the genus g. In particular, N. Hartsfield and G. Ringel’s results [J. Comb. Theory, Ser. B 46 (1989), 84-95] are generalized by way of generating minimal quadrangulations of infinitely many other genera.
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2013
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-013-2771-y