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101.
For any graph H, let Forb*(H) be the class of graphs with no induced subdivision of H. It was conjectured in [J Graph Theory, 24 (1997), 297–311] that, for every graph H, there is a function fH: ?→? such that for every graph G∈Forb*(H), χ(G)≤fH(ω(G)). We prove this conjecture for several graphs H, namely the paw (a triangle with a pendant edge), the bull (a triangle with two vertex‐disjoint pendant edges), and what we call a “necklace,” that is, a graph obtained from a path by choosing a matching such that no edge of the matching is incident with an endpoint of the path, and for each edge of the matching, adding a vertex adjacent to the ends of this edge. © 2011 Wiley Periodicals, Inc. J Graph Theory 71:49–68, 2012 相似文献
102.
We show that a moving vortex lattice, as it comes to a crystal edge, radiates into a free space the harmonics of the washboard frequency, omega(0)=2pi v/a, up to a superconducting gap, Delta/variant Planck's over 2pi. Here v is the velocity of the vortex lattice and a is the intervortex spacing. We compute radiation power and show that this effect can be used for the generation of terahertz radiation and for characterization of moving vortex lattices. 相似文献
103.
A clique-transversal of a graph G is a subset of vertices that meets all the cliques of G. A clique-independent set is a collection of pairwise vertex-disjoint cliques. A graph G is clique-perfect if the sizes of a minimum clique-transversal and a maximum clique-independent set are equal for every induced subgraph of G. The list of minimal forbidden induced subgraphs for the class of clique-perfect graphs is not known. Another open question concerning clique-perfect graphs is the complexity of the recognition problem. Recently we were able to characterize clique-perfect graphs by a restricted list of forbidden induced subgraphs when the graph belongs to two different subclasses of claw-free graphs. These characterizations lead to polynomial time recognition of clique-perfect graphs in these classes of graphs. In this paper we solve the characterization problem in two new classes of graphs: diamond-free and Helly circular-arc () graphs. This last characterization leads to a polynomial time recognition algorithm for clique-perfect graphs. 相似文献