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Suppose S is a subset of a metric spaceM with a metric δ, and D a subset of positive real numbers. The distance graph G(S, D), with a distance set D, is the graph with vertex set S in which two vertices x and y are adjacent iff δ(x, y) ∈ D. Distance graphs, first studied by Eggleton et al. , were motivated by the well-known plane-coloring problem: What… (More)
The strong chromatic index of a graph G is the minimum integer k such that the edge set of G can be partitioned into k induced matchings. Faudree et al. [R.J. Faudree, R.H. Schelp, A. Gyárfás, Zs. Tuza, The strong chromatic index of graphs, Ars Combin. 29B (1990) 205–211] proposed an open problem: If G is bipartite and if for each edge xy ∈ E(G), d(x)+ d(y)… (More)
The generalized Mycielskians (also known as cones over graphs) are the natural generalization of the Mycielski graphs (which were first introduced by Mycielski in 1955). Given a graph G and any integer m 0, one can transform G into a new graph m(G), the generalized Mycielskian of G. This paper investigates circular clique number, total domination number,… (More)
In this paper we continue our study of the Delta-group structure on the braid groups and mapping class groups of a surface. We calculate the homotopy groups of these Delta-groups and prove some results about Brunnian braid groups and Brunnian mapping class groups. This is the second of a pair of papers on these structures.
We describe a Delta-group structure on the mapping class groups of surfaces, and show that it is compatible with the Delta-group structures of the braid groups of surfaces given by Berrick-Cohen-Wong-Wu. We then prove an isomorphism theorem relating these two Delta-groups. This is the first of a pair of papers on this topic.