An extremal result for graphs with an application to their colourings.
An extremal theorem in the hypercube.
An improved bound on the minimal number of edges in color-critical graphs.
An inequality related to Vizing's conjecture.
An ordering of some metrics defined on the space of graphs
An upper bound for graphs of diameter 3 and given degree obtained as abelian lifts of dipoles
We derive an upper bound on the number of vertices in graphs of diameter 3 and given degree arising from Abelian lifts of dipoles with loops and multiple edges.
An upper bound for the minimum degree of a graph
An upper bound for the minimum valency of a graph embedded in a compact 2-manifold
An upper bound on the basis number of the powers of the complete graphs
The basis number of a graph is defined by Schmeichel to be the least integer such that has an -fold basis for its cycle space. MacLane showed that a graph is planar if and only if its basis number is . Schmeichel proved that the basis number of the complete graph is at most . We generalize the result of Schmeichel by showing that the basis number of the -th power of is at most .
Analoga of Menger's theorem for polar and polarized graphs
Another infinite sequence of dense triangle-free graphs.
Another Upper Bound For The Domination Number Of A Graph.
Antidirected Hamilton Circuits and Paths in Tournaments.
Antidomatic number of a graph.
Antidomatic number of a graph
A subset of the vertex set of a graph is called dominating in , if for each there exists adjacent to . An antidomatic partition of is a partition of , none of whose classes is a dominating set in . The minimum number of classes of an antidomatic partition of is the number of . Its properties are studied.
Application de la théorie des graphes au choix des investissements à court terme dans un réseau électrique sujet à avaries
Arbres minimums communs et compatibilité de données de types variés
Associative graph products and their independence, domination and coloring numbers
Associative products are defined using a scheme of Imrich & Izbicki [18]. These include the Cartesian, categorical, strong and lexicographic products, as well as others. We examine which product ⊗ and parameter p pairs are multiplicative, that is, p(G⊗H) ≥ p(G)p(H) for all graphs G and H or p(G⊗H) ≤ p(G)p(H) for all graphs G and H. The parameters are related to independence, domination and irredundance. This includes Vizing's conjecture directly, and indirectly the Shannon capacity of a graph...
Asymptotic bounds for bipartite Ramsey numbers.
Asymptotic comparison of two constructions for large digraphs of given degree and diameter
We compare the asymptotic growth of the order of the digraphs arising from a construction of Comellas and Fiol when applied to Faber-Moore digraphs versus plainly the Faber-Moore digraphs for the corresponding degree and diameter.