On some third parts of nearly complete digraphs

AbstractFor the complete digraph DKn with n⩾3, its half as well as its third (or near-third) part, both non-self-converse, are exhibited. A backtracking method for generating a tth part of a digraph is sketched. It is proved that some self-converse digraphs are not among the near-third parts of the complete digraph DK5 in four of the six possible cases. For n=9+6k,k=0,1,…, a third part D of DKn is found such that D is a self-converse oriented graph and all D-decompositions of DKn have trivial automorphism group

Are there any good digraph width measures?

Many width measures for directed graphs have been proposed in the last few years in pursuit of generalizing (the notion of) treewidth to directed graphs. However, none of these measures possesses, at the same time, the major properties of treewidth, namely, 1. being algorithmically useful , that is, admitting polynomial-time algorithms for a large class of problems on digraphs of bounded width (e.g. the problems definable in MSO1MSO1); 2. having nice structural properties such as being (at least nearly) monotone under taking subdigraphs and some form of arc contractions (property closely related to characterizability by particular cops-and-robber games). We investigate the question whether the search for directed treewidth counterparts has been unsuccessful by accident, or whether it has been doomed to fail from the beginning. Our main result states that any reasonable width measure for directed graphs which satisfies the two properties above must necessarily be similar to treewidth of the underlying undirected graph

An extensive English language bibliography on graph theory and its applications, supplement 1

Graph theory and its applications - bibliography, supplement

Graph Theory

This workshop focused on recent developments in graph theory. These included in particular recent breakthroughs on nowhere-zero flows in graphs, width parameters, applications of graph sparsity in algorithms, and matroid structure results

Graph Theory

[no abstract available