We resolve the following conjecture raised by Levin together with Linial, London, and Rabinovich [Combinatorica, 1995]. For a graph G, let dim(G) be the smallest d such that G occ...
A graph G is clique-perfect if the cardinality of a maximum cliqueindependent set of H is equal to the cardinality of a minimum cliquetransversal of H, for every induced subgraph ...
The cocircuit graph of an oriented matroid is the 1-skeleton of the cellular decomposition induced by the Topological Representation Theorem due to Folkman and Lawrence (1978) [J....
We shall prove that for all 3 and > 0 there exists a sparse oriented graph of arbitrarily large order with oriented girth and such that any 1/2 + proportion of its arcs induc...
Abstract—We present here a method for analyzing the neighborhoods of all the vertices in a large graph. We first give an algorithm for characterizing a simple undirected graph t...