We answer a question of Golumbic, Monma and Trotter by constructing proper tolerance graphs that are not unit tolerance graphs. An infinite family of graphs that are minimal in this respect isâ€¦ (More)

Let G be a graph with n nodes, e edges, chromatic number and girth g. In an acyclic orientation of G, an arc is dependent if its reversal creates a cycle. It is well known that if < g, then G has anâ€¦ (More)

Recently, Hedetniemi et al. introduced (1, 2)-domination in graphs, and the authors extended that concept to (1, 2)-domination graphs of digraphs. Given vertices x and y in a digraph D, x and y formâ€¦ (More)

A domination graph of a digraph D, dom(D), is created using the vertex set of D and edge {u, v} âˆˆ E[dom(D)] whenever (u, z) âˆˆ A(D) or (v, z) âˆˆ A(D) for every other vertex z âˆˆ V (D). The underlyingâ€¦ (More)

A graph is a probe interval graph (PIG) if its vertices can be partitioned into probes and nonprobes with an interval assigned to each vertex so that vertices are adjacent if and only if theirâ€¦ (More)

We construct all six-element orders which are not 50%-tolerance orders. We show that a width-two order is a 50% tolerance order if and only if no restriction of the order to a six-element set isâ€¦ (More)

A domination graph of a digraph D, dom (D), is created using thc vertex set of D and edge uv E E (dom (D)) whenever (u, z) E A (D) or (v, z) E A (D) for any other vertex z E V (D). Here, we considerâ€¦ (More)