k-Chromatic Number of Graphs on Surfaces
نویسندگان
چکیده
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 improve the previously known upper bounds, and show that in many cases, the new upper bound coincides with the lower bound obtained from embedding disjoint cliques in the surface. In the proof of this result, we derive a variant of Euler’s Formula for union of several graphs that might be interesting independently.
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عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 23 شماره
صفحات -
تاریخ انتشار 2009