The slope-number of a graph G is the minimum number of distinct edge slopes in a straight-line drawing of G in the plane. We prove that for Δ 5 and all large n, there is a Δ-reg...
The aim of this paper is to give a coherent account of the problem of constructing cubic graphs with large girth. There is a well-defined integer µ0(g), the smallest number of v...
For several graph-theoretic parameters such as vertex cover and dominating set, it is known that if their sizes are bounded by k then the treewidth of the graph is bounded by some ...
Erik D. Demaine, Fedor V. Fomin, Mohammad Taghi Ha...
Bar k-visibility graphs are graphs admitting a representation in which the vertices correspond to horizontal line segments, called bars, and the edges correspond to vertical lines...
In the Connected Dominating Set problem we are given as input a graph G and a positive integer k, and are asked if there is a set S of at most k vertices of G such that S is a dom...