Optimal connected subgraphs: Integer programming formulations and polyhedra
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DOI: 10.1002/net.22101
Abstract: Connectivity is a central concept in combinatorial optimization, graph theory, and operations research. In many applications, one is interested in finding an optimal subset of vertices with the essential requirement that the vertices are connected,… read more here.
Keywords: integer; programming formulations; connected subgraphs; optimal connected ... See more keywords
Infinitely connected subgraphs in graphs of uncountable chromatic number
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DOI: 10.1007/s00493-016-3436-4
Abstract: Erdős and Hajnal conjectured in 1966 that every graph of uncountable chromatic number contains a subgraph of infinite connectivity. We prove that every graph of uncountable chromatic number has a subgraph which has uncountable chromatic… read more here.
Keywords: connected subgraphs; uncountable chromatic; subgraphs graphs; infinitely connected ... See more keywords