A number of results are established concerning long cycles in graphs with large degree sums. Let G be a graph on n vertices such that d(x) + d(y) + d(z) 3s for all triples of independent vertices x,â€¦ (More)

We show that it is NP-hard to determine if a cubic graph G is 1-tough. We then use this result to show that for any integer t â‰¥ 1, it is NP-hard to determine if a 3 t-regular graph is t-tough. Weâ€¦ (More)

Let t â‰¥ 1 be an integer. We show that it is NP-hard to determine if an r-regular graph is t-tough for any fixed integer r â‰¥ 3 t. We also discuss the complexity of recognizing if an r-regular graph isâ€¦ (More)

Chv&tal and Hammerâ€™s article [2] has been the forerunner of many papers dealing with threshold graphs and some generalizations, such as split graphs [33, matrogenic gfaphs [4], matroidal graphs [9]â€¦ (More)

A well-known formula of Tutte and Berge expresses the size of a maximum matching in G in terms of what is usually called the deficiency of G. A subset X of G for which this deficiency is attained isâ€¦ (More)

The induced path interval J (u; v) consists of the vertices on the induced paths between u and v in a connected graph G. Di-erences in properties with the geodesic interval are studied. Those graphsâ€¦ (More)

The P4-sparse Graph Sandwich Problem asks, given two graphs G 1 = (V, E1) and G2 = (V, E2), whether there exists a graph G = (V, E) such that E1 âŠ† E âŠ† E2 and G is P4-sparse. In this paper we presentâ€¦ (More)