Strengthening topological colorful results for graphs |
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| Institution: | 1. School of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran;2. Department of Mathematical Sciences, Shahid Beheshti University, P.O. Box 19839-69411, Tehran, Iran;3. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran;4. Université Paris Est, CERMICS, 77455 Marne-la-Vallée CEDEX, France |
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| Abstract: | Various results ensure the existence of large complete and colorful bipartite graphs in properly colored graphs when some condition related to a topological lower bound on the chromatic number is satisfied. We generalize three theorems of this kind, respectively due to Simonyi and Tardos 2006), Simonyi et al. (2013), and Chen 2011). As a consequence of the generalization of Chen’s theorem, we get new families of graphs whose chromatic number equals their circular chromatic number and that satisfy Hedetniemi’s conjecture for the circular chromatic number. |
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