منابع مشابه
Perfect graphs are kernel solvable
In this paper we prove that perfect graphs are kernel solvable, as it was conjectured by Berge and Duchet (1983). The converse statement, i.e. that kernel solvable graphs are perfect, was also conjectured in the same paper, and is still open. In this direction we prove that it is always possible to substitute some of the vertices of a non-perfect graph by cliques so that the resulting graph is ...
متن کاملParity graphs are kernel-M-solvable
While the famous Berge’s Strong Perfect Graph Conjecture (see [l] for details on perfect graphs) remains a major unsolved problem in Graph Theory, an alternative characterization of Perfect Graphs was conjectured in 1982 by Berge and the author [3]. This second conjecture asserts the existence of kernels for a certain type of orientations of perfect graphs. Here we prove a weaker form of the co...
متن کاملSTS-graphs of perfect codes mod kernel
We show that a 1-error-correcting code C is ‘foldable’ over its kernel via the Steiner triple systems associated to the codewords whenever C is perfect. The resulting ‘folding’ produces a graph invariant that for Vasil’ev codes of length 15 is complete, showing in particular that there exist nonadditive propelinear codes and just one nonlinear Vasil’ev additive code up to equivalence.
متن کاملOn kernel-perfect orientations of line graphs
We exploit the technique of Galvin (1995) to prove that an orientation D of a line-graph G (of a multigraph) is kernel-perfect if and only if every oriented odd cycle in D has a chord (or pseudochord) and every clique has a kernel. @ 1998 Elsevier Science B.V. All rights reserved
متن کاملOn a class of kernel-perfect and kernel-perfect-critical graphs
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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1996
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00096-f