An ordering of some metrics defined on the space of graphs
An upper bound for the minimum degree of a graph
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 .
An upper bound on the domination number of a graph.
Analoga of Menger's theorem for polar and polarized graphs
Analysis of a class of graph partitioning problems
Another Upper Bound For The Domination Number Of A Graph.
Antichains in the homomorphism order of graphs
Let and , respectively, denote the partially ordered sets of homomorphism classes of finite undirected and directed graphs, respectively, both ordered by the homomorphism relation. Order theoretic properties of both have been studied extensively, and have interesting connections to familiar graph properties and parameters. In particular, the notion of a duality is closely related to the idea of splitting a maximal antichain. We construct both splitting and non-splitting infinite maximal antichains...
Application de l'algèbre de Boole à l'étude des graphes
Applications harmoniques entre graphes finis et un théorème de superrigidité
Applications of combinatorics to statics – a survey
Aspects topologiques de la séperation dans les graphes infinis. I.
Aspects topologiques de la séperation dans les graphes infinis. II.
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...
Associative Products of Graphs.
Asymptotical estimation of some characteristics of finite graphs
Asymptotische Abschätzung einer Anzahlfunktion in endlichen Relationssystemen.
Atomic compactness for reflexive graphs
A first order structure with universe M is atomic compact if every system of atomic formulas with parameters in M is satisfiable in provided each of its finite subsystems is. We consider atomic compactness for the class of reflexive (symmetric) graphs. In particular, we investigate the extent to which “sparse” graphs (i.e. graphs with “few” vertices of “high” degree) are compact with respect to systems of atomic formulas with “few” unknowns, on the one hand, and are pure restrictions of their...
Automorphismen von polyedrischen Graphen.
-valuations of graphs