Let G be a connected, locally connected, claw-free graph of order n and x, y be two vertices of G. In this paper, we prove that if for any 2-cut S of G, S {x, y} = , then each (x...
We prove that it is NP-complete to decide whether a bipartite graph of maximum degree three on nk vertices can be partitioned into n paths of length k. Finally, we propose some ap...
Abstract— This paper presents a genetic algorithmic approach for finding efficient paths in directed graphs when optimizing multiple objectives. Its aim is to provide solutions...
We introduce and study backbone colorings, a variation on classical vertex colorings: Given a graph G = (V, E) and a spanning subgraph H of G (the backbone of G), a backbone color...
Hajo Broersma, Fedor V. Fomin, Petr A. Golovach, G...
We provide the first linear-space data structure with provable sublinear query time for exact point-topoint shortest path queries in planar graphs. We prove that for any planar gr...