Displaying similar documents to “Independence complexes of stable Kneser graphs.”

On the Vertex Separation of Cactus Graphs

Markov, Minko (2007)

Serdica Journal of Computing

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This paper is part of a work in progress whose goal is to construct a fast, practical algorithm for the vertex separation (VS) of cactus graphs. We prove a theorem for cacti", a necessary and sufficient condition for the VS of a cactus graph being k. Further, we investigate the ensuing ramifications that prevent the construction of an algorithm based on that theorem only.

On the Vertex Separation of Maximal Outerplanar Graphs

Markov, Minko (2008)

Serdica Journal of Computing

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We investigate the NP-complete problem Vertex Separation (VS) on Maximal Outerplanar Graphs (mops). We formulate and prove a “main theorem for mops”, a necessary and sufficient condition for the vertex separation of a mop being k. The main theorem reduces the vertex separation of mops to a special kind of stretchability, one that we call affixability, of submops.

Parity vertex colouring of graphs

Piotr Borowiecki, Kristína Budajová, Stanislav Jendrol', Stanislav Krajci (2011)

Discussiones Mathematicae Graph Theory

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A parity path in a vertex colouring of a graph is a path along which each colour is used an even number of times. Let χₚ(G) be the least number of colours in a proper vertex colouring of G having no parity path. It is proved that for any graph G we have the following tight bounds χ(G) ≤ χₚ(G) ≤ |V(G)|-α(G)+1, where χ(G) and α(G) are the chromatic number and the independence number of G, respectively. The bounds are improved for trees. Namely, if T is a tree with diameter diam(T) and...

Weak Saturation Numbers for Sparse Graphs

Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson (2013)

Discussiones Mathematicae Graph Theory

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For a fixed graph F, a graph G is F-saturated if there is no copy of F in G, but for any edge e ∉ G, there is a copy of F in G + e. The minimum number of edges in an F-saturated graph of order n will be denoted by sat(n, F). A graph G is weakly F-saturated if there is an ordering of the missing edges of G so that if they are added one at a time, each edge added creates a new copy of F. The minimum size of a weakly F-saturated graph G of order n will be denoted by wsat(n, F). The graphs...