A weighted graph G is called well-covered if all its maximal independent sets have the same weight. Let S be an independent set of G (possibly, S = ∅). The subgraph G − N [S] is called a co-stable subgraph of G. We denote by CSub(G) the set of all co-stable subgraphs of G considered up to isomorphism. A class of weighted graphs P is called co-hereditary if it is closed under taking co-stable su...

A quasi-line graph is a graph in which the neighbourhood of any vertex can be covered by two cliques; every line graph is a quasi-line graph. Reed conjectured that for any graph G, χ(G) ≤ d12(∆(G) + 1 + ω(G))e [13]. We prove that the conjecture holds if G is a quasi-line graph, extending a result of King, Reed and Vetta, who proved the conjecture for line graphs [8], and improving the bound of ...

According to static models of industrial organization, a rise in competition decreases prices. In this paper, I test whether this conclusion can be reversed in the mobile telecommunications markets where dynamic e ciency e ects might be signi cant. The empirical test relies on the change in the intensity of competition introduced by the entry of the fourth mobile operator in France and the merg...

The stability number α(G) of the graph G is the size of a maximum stable set of G. If sk denotes the number of stable sets of cardinality k in graph G, then I(G;x) = s0 + s1x + ... + sαx α is the independence polynomial of G [12], where α = α(G) is the size of a maximum stable set. In this paper we prove that I(G;−1) satisfies |I(G;−1)| ≤ 2, where ν(G) equals the cyclomatic number of G, and the...

A linear forest is the union of a set of vertex disjoint paths. Akiyama, Exoo and Harary and independently Hilton have conjectured that the edges of every graph of maximum degree ∆ can be covered by d∆+1 2 e linear forests. We show that almost every graph can be covered with this number of linear forests. 1 Linear Forests, Directed Cycles, and the Probabilistic Method A linear forest is the uni...

G is a well-covered graph provided all its maximal stable sets are of the same size (Plummer, 1970). S is a local maximum stable set of G, and we denote by S ∈ Ψ(G), if S is a maximum stable set of the subgraph induced by S ∪ N(S), where N(S) is the neighborhood of S. In 2002 we have proved that Ψ(G) is a greedoid for every forest G. The bipartite graphs and the trianglefree graphs, whose famil...

Since Kronecker Product Graph Model (KPGM) was introduced, it has been widely used to model real networks. The characteristics of the model specially its single fractal structure have made KPGM one of the most important algorithm of the last years. However, the utilization of a single fractal structure decreases the potential of KPGM by limiting the graph space covered by the model. In this pap...

Owing to the inhomogeneity and ill defined edges present in images, the incorporation of prior knowledge into level set models, in image segmentation, is a field of active researches. In this paper, a new way of incorporating prior information to constrain the evolution of the level set model during the segmentation is presented. This technique allows resolving the problem of applying the same ...