๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Minimal imperfect graphs: A simple approach

โœ Scribed by G. S. Gasparian


Publisher
Springer-Verlag
Year
1996
Tongue
English
Weight
199 KB
Volume
16
Category
Article
ISSN
0209-9683

No coin nor oath required. For personal study only.


๐Ÿ“œ SIMILAR VOLUMES


The connectivity of minimal imperfect gr
โœ Seb๏ฟฝ, Andr๏ฟฝs ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 535 KB

We prove that partitionable graphs are 2w -2-connected, that this bound is sharp, and prove some structural properties of cutsets of cardinality 2w -2. The proof of the connectivity result is a simple linear algebraic proof.

On transversals in minimal imperfect gra
โœ Jean-Luc Fouquet; Frรฉdรฉric Maire; Irena Rusu; Henri Thuillier ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 885 KB

proved that no minimal imperfect graph has a small transversal, that is, a set of vertices of cardinality at most x + M-1 which meets every c+clique and every x-stable set. In this paper we prove that a slight generalization of this notion of small transversal leads to a conjecture which is as stro

On minimal imperfect graphs with circula
โœ Bacs๏ฟฝ, G๏ฟฝbor; Boros, Endre; Gurvich, Vladimir; Maffray, Fr๏ฟฝd๏ฟฝric; Preissmann, My ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 293 KB

Results of Lovรกsz and Padberg entail that the class of so-called partitionable graphs contains all the potential counterexamples to Berge's famous Strong Perfect Graph Conjecture, which asserts that the only minimal imperfect graphs are the odd chordless cycles with at least five vertices (''odd hol

About Skew Partitions in Minimal Imperfe
โœ F. Roussel; P. Rubio ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 188 KB

V. Chva tal conjectured in 1985 that a minimal imperfect graph G cannot have a skew cutset (i.e., a cutset S decomposable into disjoint sets A and B joined by all possible edges). We prove here the conjecture in the particular case where at least one of A and B is a stable set. 2001 Elsevier Science