Colorful subgraphs in Kneser-like graphs
نویسندگان
چکیده
منابع مشابه
Colorful subgraphs in Kneser-like graphs
Combining Ky Fan’s theorem with ideas of Greene and Matoušek we prove a generalization of Dol’nikov’s theorem. Using another variant of the Borsuk-Ulam theorem due to Bacon and Tucker, we also prove the presence of all possible completely multicolored t-vertex complete bipartite graphs in t-colored t-chromatic Kneser graphs and in several of their relatives. In particular, this implies a genera...
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Using a Zq-generalization of a theorem of Ky Fan, we extend to Kneser hypergraphs a theorem of Simonyi and Tardos that ensures the existence of multicolored complete bipartite graphs in any proper coloring of a Kneser graph. It allows to derive a lower bound for the local chromatic number of Kneser hypergraphs (using a natural definition of what can be the local chromatic number of a uniform hy...
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Kierstead, H.A. and W.T. Trotter. Colorful induced subgraphs, Discrete Mathematics 101 (1992) 165-169. A colored graph is a graph whose vertices have been properly, though not necessarily optimally colored, with integers. Colored graphs have a natural orientation in which edges are directed from the end point with smaller color to the end point with larger color. A subgraph of a colored graph i...
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We prove that for a large family of product graphs, and for Kneser graphs K(n, αn) with fixed α < 1/2, the following holds. Any set of vertices that spans a small proportion of the edges in the graph can be made independent by removing a small proportion of the vertices of the graph. This allows us to strengthen the results of [DFR08] and [DF09], and show that any independent set in these graph...
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The vertex set of a Kneser graph KG(m,n) consists of all n-subsets of the set [m] = {0, 1, . . . ,m − 1}. Two vertices are defined to be adjacent if they are disjoint as subsets. A subset of [m] is called 2stable if 2 ≤ |a − b| ≤ m − 2 for any distinct elements a and b in that subset. The reduced Kneser graph KG2(m,n) is the subgraph of KG(m,n) induced by vertices that are 2-stable subsets. We ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2007
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2007.04.015