Let G be a series-parallel graph with integer edge weights. A p-coloring of G is a mapping of vertices of G into Zp (ring of integers modulo p) so that the distance between colors of adjacent vertices u and v is at least the weight of the edge uv. We describe a quadratic time p-coloring algorithm where p is either twice the maximum edge weight or the largest possible sum of three weights of edg...

We show that every digraph D with minimum outdegree 6 and maximum indegree A contains a directed cycle of length O(mod k), provided e[dd+ l](1-l/k) " < 1. In particular, if A < (2 "-e)/e6 then D contains an even cycle. 0 1989 Academic Press, Inc.

In the context of graph transformations we look at the operation of switching, which can be viewed as an elegant method for realizing global transformations of graphs through local transformations of the vertices. A switching class is then a set of graphs obtainable from a given start graph by applying the switching operation. Continuing the line of research in Ehrenfeucht et al. we consider th...

The notion of travel groupoids was introduced by L. Nebeský in 2006 in connection with a study on geodetic graphs. A travel groupoid is a pair of a set V and a binary operation ∗ on V satisfying two axioms. For a travel groupoid, we can associate a graph. We say that a graph G has a travel groupoid if the graph associated with the travel groupoid is equal to G. Nebeský gave a characterization f...

The hamiltonian index of a graph G is the smallest integer k such that the k th iterated line graph of G is hamiltonian We rst show that with one exceptional case adding an edge to a graph cannot increase its hamiltonian index We use this result to prove that neither the contraction of an AG F contractible subgraph F of a graph G nor the closure operation performed on G if G is claw free a ects...

Characterising graph classes by forbidding a set of graphs has been a common feature in graph theory for many years. Up to date many classes have been char-acterised with respect to the induced subgraph relation and there are a plethora of results regarding graph classes closed under the minor relation. We consider the characterisation of graph classes closed under partial orders including edge...

In this paper, we present SGDB, a graph database with a storage model optimized for computation of Spreading Activation (SA) queries. The primary goal of the system is to minimize the execution time of spreading activation algorithm over large graph structures stored on a persistent media; without pre-loading the whole graph into the memory. We propose a storage model aiming to minimize number ...

Context-free hypergraph grammars and boundary graph grammars of bounded nonterminal degree have the same power, both for generating sets of graphs and for generating sets of hypergraphs. Arbitrary boundary graph grammars have more graph generating power than context-free hypergraph grammars, but they have the same hypergraph generating power. To obtain these results, several normal forms for bo...

We propose broadcasting algorithms for line digraphs in the te lephone model The new protocols use a broadcasting protocol for a graph G to obtain a broadcasting protocol for the graph LG the graph obtained by applying k times the line digraph operation to G As a consequence improved bounds for the broadcasting time in De Bruijn Kautz and Wrapped Butter y digraphs are obtained

Given the degree sequence d of a graph, the realization graph of d is the graph having as its vertices the labeled realizations of d, with two vertices adjacent if one realization may be obtained from the other via an edge-switching operation. We describe a connection between Cartesian products in realization graphs and the canonical decomposition of degree sequences described by R.I. Tyshkevic...