Let G be a graph with n vertices and independence number α. Hadwiger’s conjecture implies that G contains a clique minor of order at least n/α. In 1982, Duchet and Meyniel proved that this bound holds within a factor 2. Our main result gives the first improvement on their bound by an absolute constant factor. We show that G contains a clique minor of order larger than .504n/α. We also prove rel...

Strongly perfect graphs were introduced by C. Berge and P. Duchet in [1]. In [4], [3] the following was studied: the problem of strong perfectness for the Cartesian product, the tensor product, the symmetrical difference of n, n ≥ 2, graphs and for the generalized Cartesian product of graphs. Co-strong perfectness was first studied by G. Ravindra and D. Basavayya [5]. In this paper we discuss s...

née dans les années soixante, la sociocritique cherche à faire sortir le réel social à travers le texte littéraire. de nombreuses perspectives ont été ouvertes par des sociocritiques, parmi lesquelles, celle de duchet semble la plus textuelle. pour lui, la sociocritique est plutôt une analyse socio-sémiotique du texte littéraire. la littérature contemporaine d’iran, influencée par les changemen...

The concept of (k, l)-kernels of digraphs was introduced in [2]. Next, H. Galeana-Sanchez [?] proved a sufficient condition for a digraph to have a (k, l)-kernel. The result generalizes the well-known theorem of P. Duchet and it is formulated in terms of symmetric pairs of arcs. Our aim is to give necessary and sufficient conditions for digraphs without symmetric pairs of arcs to have a (k, l)-...

In 1980 Piere Duchet conjectured that odd directed cycles are the only edge minimal kernel-less connected digraphs i.e. in which after the removal of any edge a kernel appears. Although this conjecture was disproved recently by Apartsin, Ferapontova and Gurvich (1996), the following modiication of Duchet's conjecture still holds: odd holes (i.e. odd non-directed chordless cycles of length 5 or ...

This paper develops new combinatorial and geometric techniques for studying the topology of the real semialgebraic variety 31 (M) of all realizations of an oriented matroid M . We focus our attention on point configurations in general position, and as the main result we prove that the realization space of every uniform rank 3 oriented matroid with up to eight points is contractible. For these s...

A kernel of a directed graph D is defined as an independent set which is reachable from each outside vertex by an arc. A graph G is called kernel-solvable if an orientation D of G has a kernel whenever each clique of G has a kernel in D. The notion of kernel-solvability has important applications in combinatorics, list coloring, and game theory. It turns out that kernel-solvability is equivalen...

Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A kernel N of D is an independent set of vertices such that for every w∈V (D) − N there exists an arc from w to N . A digraph D is called right-pretransitive (resp. left-pretransitive) when (u; v)∈A(D) and (v; w)∈A(D) implies (u; w)∈A(D) or (w; v)∈A(D) (resp. (u; v)∈A(D) and (v; w)∈A(D) implies (u; ...