Jean-Marie Laborde

Another characterization of hypercubes

Nous montrons que dans la classe des graphes connexes tels que deux aretes incidentes quelconques appartiennent a un et un seul quadrilatere, les hypercubes finis sont les graphes de degre minimum n fini et possedant 2^n sommets. The following theorem^1 is proved: Let C be the class connected graphs such that each pair of distinct adjacent edges lies in exactly one 4-cycle. Then G in C is a finite hypercube ifthe minimum degree @d of G is finite and^2 |V(G)| = 2^@d.

Spanning caterpillars of a hypercube

Spanning trees of the hypercube Qn have been recently studied by several authors. In this paper, we construct spanning trees of Qn which are caterpillars and establish quantitative bounds for a caterpillar to span Qn. As a corollary, we disprove a conjecture of Harary and Lewinter on the length of the spine of a caterpillar spanning Qn.

Distance monotone graphs and a new characterization of hypercubes

Abstract The aim of this paper is to study the class of s.c. distance monotone graphs which arise naturally when investigating some intersection properties of graphs. A new characterization of hypercubes is also obtained.

Cartesian products of trees and paths

We characterize the (weak) Cartesian products of trees among median graphs by a forbidden 5-vertex convex subgraph. The number of tree factors (if finite) is half the length of a largest isometric cycle. Then a characterization of Cartesian products of n trees obtains in terms of isometric cycles and intervals. Finally we investigate to what extent the proper intervals determine the product structure.

On the domatic number of the n-cube and a conjecture of Zelinka (French)

Recently Zelinka [6] proved that d ( Q n ), the domatic number of the n -cube, is for n equal 2 p − 1 or n equal 2 p , exactly 2 p . We show here how d ( Q n ) can be determined for the preceding values, in a very simple way. We then disprove a conjecture by Zelinka and replace it by another closely related to a former one, involving the domination number of the n -cube.

On posets of m -ary words

Abstract The posetBm, n, which consists of the naturally ordered subwords of the cyclic word on length n on an alphabet of m letters, where subwords are obtained by deleting letters, is introduced and studied. This poset is of special interest since it is strongly related to several different structured posets, like Boolean lattices, chains, Higman orders and Kruskal-Katona posets.

Some Intersection Theorems for Structures

This paper deals with intersection properties for structures extending earlier results by M. Simonovits and V. T. Sos. One of the results asserts that for a given graph G = (V, E) with girth r (satisfying some additional technical assumption), if G1, . . ., GN is a family of its subgraphs with property Gi � Gjis a cycle for all 1 ≤ i

Characterization of grid graphs

Abstract In this paper we are mainly interested in the characterization of grid graphs i.e. products of paths.

Regularisation numerique d'orbites

Abstract Given a permutation group G acting on a set X we consider the orbits of the induced group on P (X) . This paper is concerned with the following question: what conditions are involved in the frequently observed fact that the number of orbits grows as 2 | x | /| G | for large | X |?

Sur le cardinal maximum de la base complete d'une fonction booleenne, en fonction du nombre de conjonctions de l'une de ses formes normales.

A.K. Chandra et G. Markowski [1] showed that any Boolean expression in disjunctive normal form having k conjuncts can have at most f(k) implicants, where f(k) satisfies 3^@?^k^3^@?=