Facets of conflict hypergraphs
نویسنده
چکیده
Dedicated to that mysterious Power: Who requires odd holes for imperfection in graphs And ensures unimodularity of network flows Who converges large numbers towards normality And lets greediness work for the spanning tree Who animates the intelligence inside us And creates the world-illusion around us She is the seed of all creativity And without Her grace This work would forever remain a mere potentiality iii ACKNOWLEDGEMENTS I would like to thank the following persons for their advice and support:
منابع مشابه
Unique-Maximum and Conflict-Free Coloring for Hypergraphs and Tree Graphs
We investigate the relationship between two kinds of vertex colorings of hypergraphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every hyperedge of the hypergraph the maximum color in the hyperedge occurs in only one vertex of the hyperedge. In a conflict-free coloring, in every hyperedge of the hypergraph there exists a co...
متن کاملOn the maximum feasible subsystem problem, IISs and IIS-hypergraphs
We consider the MAX FS problem: For a given infeasible linear system Ax ≤ b, determine a feasible subsystem containing as many inequalities as possible. This problem, which is NP-hard and also difficult to approximate, has a number of interesting applications in a wide range of fields. In this paper we examine structural and algorithmic properties of MAX FS and of Irreducible Infeasible Subsyst...
متن کاملConflict-free Colorings of Uniform Hypergraphs with Few Edges
A coloring of the vertices of a hypergraph H is called conflict-free if each edge e of H contains a vertex whose color does not repeat in e. The smallest number of colors required for such a coloring is called the conflict-free chromatic number of H, and is denoted by χCF (H). Pach and Tardos proved that for an (2r − 1)-uniform hypergraph H with m edges, χCF (H) is at most of the order of rm lo...
متن کاملConflict-Free Colourings of Uniform Hypergraphs With Few Edges
A coloring of the vertices of a hypergraph H is called conflict-free if each edge e of H contains a vertex whose color does not get repeated in e. The smallest number of colors required for such a coloring is called the conflict-free chromatic number of H, and is denoted by χCF (H). Pach and Tardos studied this parameter for graphs and hypergraphs. Among other things, they proved that for an (2...
متن کاملBrooks type results for conflict-free colorings and {a, b}-factors in graphs
A vertex-coloring of a hypergraph is conflict-free, if each edge contains a vertex whose color is not repeated on any other vertex of that edge. Let f(r,∆) be the smallest integer k such that each r-uniform hypergraph of maximum vertex degree ∆ has a conflict-free coloring with at most k colors. As shown by Tardos and Pach, similarly to a classical Brooks’ type theorem for hypergraphs, f(r,∆) ≤...
متن کامل