A simple matrix is a (0,1)-matrix with no repeated columns. For a (0,1)-matrix F , we say that a (0,1)-matrix A has F as a Berge hypergraph if there is a submatrix B of A and some row and column permutation of F , say G, with G 6 B. Letting ‖A‖ denote the number of columns in A, we define the extremal function Bh(m,F ) = max{‖A‖ : A m-rowed simple matrix and no Berge hypergraph F}. We determine...

We introduce the process number of a digraph as a tool to study rerouting issues in wdm networks. This parameter is closely related to the vertex separation (or pathwidth). We consider the recognition and the characterization of (di)graphs with small process number. In particular, we give a linear time algorithm to recognize (and process) graphs with process number at most 2, along with a chara...

In [2], Brousek characterizes all triples of connected graphs, G1, G2, G3, with Gi = K1,3 for some i = 1, 2, or 3, such that all G1G2G3free graphs contain a hamiltonian cycle. In [8], Faudree, Gould, Jacobson and Lesniak consider the problem of finding triples of graphs G1, G2, G3, none of which is a K1,s, s ≥ 3 such that G1G2G3-free graphs of sufficiently large order contain a hamiltonian cycl...

The substitution composition of two disjoint graphs G1 and G2 is obtained by first removing a vertex x from G2 and then making every vertex in G1 adjacent to all neighbours of x in G2. Let F be a family of graphs defined by a set Z of forbidden configurations. Giakoumakis [V. Giakoumakis, On the closure of graphs under substitution, Discrete Mathematics 177 (1997) 83–97] proved that F, the clos...

A spanning tree with no vertices of degree two is called a homeomorphically irreducible spanning tree (or a HIST ) of a graph. In [7], sets of forbidden subgraphs that imply the existence of a HIST in a connected graph of sufficiently large order were characterized. In this paper, we focus on characterizing connected P5-free graphs which have a HIST. As applications of our main result, we also ...

For any connected undirected graph G, let (G) be the graph invariant introduced by Colin de Verdi ere. In this paper we study the behaviour of (G) under clique sums of graphs. In particular, we give a forbidden minor characterization of those clique sums G of G 1 and G 2 for which (G) = maxf(G 1); (G 2)g.

In this paper, we introduce the notion of path-bicolorability that generalizes bipartite graphs in a natural way: For k ≥ 2, a graph G = (V,E) is Pk-bicolorable if its vertex set V can be partitioned into two subsets (i.e., colors) V1 and V2 such that for every induced Pk (i.e., path with exactly k − 1 edges and k vertices) in G, the two colors alternate along the Pk, i.e., no two consecutive v...

Edge-Path-Tree graphs are intersection graphs of Edge-Path-Tree matrices that is matrices whose columns are incidence vectors of edge-sets of paths in a given tree. Edge-Path-Tree graphs have polynomially many cliques as proved in [4] and [7]. Therefore, the problem of finding a clique of maximum weight in these graphs is solvable in strongly polynomial time. In this paper we extend this result...

Connected vertex covers are found in many applications, and the relationship between those two graph invariants is therefore a natural question to investigate. For that purpose, we introduce the Price of Connectivity, defined as the ratio between the two vertex cover numbers. We prove that the price of connectivity is at most 2 for arbitrary graphs. We further consider graph classes in which th...

Quasicontinuity is a generalisation of Scott’s notion of continuous domain, introduced in the early 80s by Gierz, Lawson and Stralka. In this paper we ask which cartesian closed full subcategories exist in qCONT, the category of all quasicontinuous domains and Scottcontinuous functions. The surprising, and perhaps disappointing, answer turns out to be that all such subcategories consist entirel...