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...
We study variants of the vertex disjoint paths problem in planar graphs where paths have to be selected from a given set of paths. We study the problem as a decision, maximization...
: This article proves the following result: Let G and G be graphs of orders n and n , respectively. Let G be obtained from G by adding to each vertex a set of n degree 1 neighbors....
Recent interest in region based image coding has given rise to graph coloring based partition encoding methods. These methods are based on the four color theorem for planar graphs...
Abstract. Bidimensionality provides a tool for developing subexponential fixed-parameter algorithms for combinatorial optimization problems on graph families that exclude a minor....
Erik D. Demaine, Mohammad Taghi Hajiaghayi, Dimitr...