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1.
Rose Morris-Wright 《Journal of Pure and Applied Algebra》2021,225(1):106468
Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results of Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC-type Artin groups. We show that the class of finite type parabolic subgroups is closed under intersection. We also study an analog of the curve complex for mapping class group constructed by Cumplido et al. using parabolic subgroups. We extend the construction of this complex, called the complex of parabolic subgroups, to FC-type Artin groups. We show that this simplicial complex is, in most cases, infinite diameter and conjecture that it is δ-hyperbolic. 相似文献
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《Discrete Mathematics》2020,343(12):112117
Let be an edge-colored graph of order . The minimum color degree of , denoted by , is the largest integer such that for every vertex , there are at least distinct colors on edges incident to . We say that an edge-colored graph is rainbow if all its edges have different colors. In this paper, we consider vertex-disjoint rainbow triangles in edge-colored graphs. Li (2013) showed that if , then contains a rainbow triangle and the lower bound is tight. Motivated by this result, we prove that if and , then contains two vertex-disjoint rainbow triangles. In particular, we conjecture that if , then contains vertex-disjoint rainbow triangles. For any integer , we show that if and , then contains vertex-disjoint rainbow triangles. Moreover, we provide sufficient conditions for the existence of edge-disjoint rainbow triangles. 相似文献
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《Discrete Mathematics》2019,342(3):623-627
Wang and Lih (2002) conjectured that every planar graph without adjacent triangles is 4-choosable. In this paper, we prove that every planar graph without any 4-cycle adjacent to two triangles is DP-4-colorable, which improves the results of Lam et al. (1999), Cheng et al. (2016) and Kim and Yu [ arXiv:1709.09809v1]. 相似文献
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《Discrete Mathematics》2019,342(2):339-343
A strong edge-coloring of a graph is a partition of its edge set into induced matchings. Let be a connected planar graph with girth and maximum degree . We show that either is isomorphic to a subgraph of a very special -regular graph with girth , or has a strong edge-coloring using at most colors. 相似文献
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We examine two criteria for balance of a gain graph, one based on binary cycles and one on circles. The graphs for which each criterion is valid depend on the set of allowed gain groups. The binary cycle test is invalid, except for forests, if any possible gain group has an element of odd order. Assuming all groups are allowed, or all abelian groups, or merely the cyclic group of order 3, we characterize, both constructively and by forbidden minors, the graphs for which the circle test is valid. It turns out that these three classes of groups have the same set of forbidden minors. The exact reason for the importance of the ternary cyclic group is not clear. © 2005 Wiley Periodicals, Inc. J Graph Theory 相似文献