616 research outputs found
Convex Cycle Bases
Convex cycles play a role e.g. in the context of product graphs. We introduce convex cycle bases and describe a polynomial-time algorithm that recognizes whether a given graph has a convex cycle basis and provides an explicit construction in the positive case. Relations between convex cycles bases and other types of cycles bases are discussed. In particular we show that if G has a unique minimal cycle bases, this basis is convex. Furthermore, we characterize a class of graphs with convex cycles bases that includes partial cubes and hence median graphs. (authors' abstract)Series: Research Report Series / Department of Statistics and Mathematic
Square Property, Equitable Partitions, and Product-like Graphs
Equivalence relations on the edge set of a graph that satisfy restrictive
conditions on chordless squares play a crucial role in the theory of Cartesian
graph products and graph bundles. We show here that such relations in a natural
way induce equitable partitions on the vertex set of , which in turn give
rise to quotient graphs that can have a rich product structure even if
itself is prime.Comment: 20 pages, 6 figure
A Short Note on Undirected Fitch Graphs
The symmetric version of Fitch's xenology relation coincides with class of
complete multipartite graph and thus cannot convey any non-trivial phylogenetic
information
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