A hypergraphH is said to be p-Helly when every p-wise intersecting partial hypergraph H′ of H has nonempty total intersection. Such hypergraphs have been characterized by Berge and Duchet in 1975, and since then they have appeared in the literature in several contexts, especially for the case p = 2, in which they are referred simply as Helly hypergraphs. An interesting generalization of p-Helly...

In this paper we give a characterization of kernel-perfect (and of critical kernel-imperfect) arc-local tournament digraphs. As a consequence, we prove that arc-local tournament digraphs satisfy a strenghtened form of the following interesting conjecture which constitutes a bridge between kernels and perfectness in digraphs, stated by C. Berge and P. Duchet in 1982: a graph G is perfect if and ...

Abstract Within the context of a special section Journal Refugee Studies, this article charts and evaluates work UK-based NGO, World University Service (WUS), in assisting Chileans who fled their country wake 1973 coup subsequent Pinochet dictatorship. The combines documentary research WUS archive, Modern Records Centre, Warwick, series in-depth interviews with 26 were assisted by WUS. It begin...

Strongly perfect graphs have been studied by several authors (e.g., Berge and Duchet [1], Ravindra [7], Wang [8]). In a series of two papers, the current paper being the second one, we investigate a fractional relaxation of strong perfection. Motivated by a wireless networking problem, we consider claw-free graphs that are fractionally strongly perfect in the complement. We obtain a forbidden i...

A graph H is a minor of a graph G if H can be obtained from a subgraph of G by contracting edges. Let t ≥ 1 be an integer, and let G be a graph on n vertices with no minor isomorphic to Kt+1. Kostochka conjectures that there exists a constant c = c(k) independent of G such that the complement of G has a minor isomorphic to Ks, where s = d2 (1 + 1/t)n − ce. We prove that Kostochka’s conjecture i...

Strongly perfect graphs have been studied by several authors (e.g. Berge and Duchet [1], Ravindra [12], Wang [14]). In a series of two papers, the current paper being the first one, we investigate a fractional relaxation of strong perfection. Motivated by a wireless networking problem, we consider claw-free graphs that are fractionally strongly perfect in the complement. We obtain a forbidden i...

Chilakamarri, K.B. and P. Hamburger, On a class of kernel-perfect and kernel-perfect-critical graphs, Discrete Mathematics 118 (1993) 253-257. In this note we present a construction of a class of graphs in which each of the graphs is either kernel-perfect or kernel-perfect-critical. These graphs originate from the theory of games (Von Neumann and Morgenstern). We also find criteria to distingui...

In this paper, we study r-uniform hypergraphs H without cycles of length less than five, employing the definition of a hypergraph cycle due to Berge. In particular, for r = 3, we show that if H has n vertices and a maximum number of edges, then |H| = 1 6 n + o(n). This also asymptotically determines the generalized Turán number T3(n, 8, 4). Some results are based on our bounds for the maximum s...