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T -preserving homomorphisms of oriented graphs

Jaroslav Nešetřil, Eric Sopena, Laurence Vignal (1997)

Commentationes Mathematicae Universitatis Carolinae

A homomorphism of an oriented graph G = ( V , A ) to an oriented graph G ' = ( V ' , A ' ) is a mapping ϕ from V to V ' such that ϕ ( u ) ϕ ( v ) is an arc in G ' whenever u v is an arc in G . A homomorphism of G to G ' is said to be T -preserving for some oriented graph T if for every connected subgraph H of G isomorphic to a subgraph of T , H is isomorphic to its homomorphic image in G ' . The T -preserving oriented chromatic number χ → T ( G ) of an oriented graph G is the minimum number of vertices in an oriented graph G ' such that there exists a T -preserving...

Teória grafov v chémii

Vladimír Baláž, Vladimír Kvasnička, Jiří Pospíchal (1991)

Pokroky matematiky, fyziky a astronomie

Tessellations of random maps of arbitrary genus

Grégory Miermont (2009)

Annales scientifiques de l'École Normale Supérieure

We investigate Voronoi-like tessellations of bipartite quadrangulations on surfaces of arbitrary genus, by using a natural generalization of a bijection of Marcus and Schaeffer allowing one to encode such structures by labeled maps with a fixed number of faces. We investigate the scaling limits of the latter. Applications include asymptotic enumeration results for quadrangulations, and typical metric properties of randomly sampled quadrangulations. In particular, we show that scaling limits of these...

Testing Cayley graph densities

Goulnara N. Arzhantseva, Victor S. Guba, Martin Lustig, Jean-Philippe Préaux (2008)

Annales mathématiques Blaise Pascal

We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an m -generated group is amenable if and only if the density of the corresponding Cayley graph equals to 2 m . We test amenable and non-amenable...

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