Maxmaxflow and counting subgraphs

Details Maxmaxflow and counting subgraphs Maxmaxflow and counting subgraphs

2007-03-20

arxiv.org/abs/math/0703585v1

Mathematics

Combinatorics

Latex2e, 47 pages (includes 2 figures)

Scientific paper

We introduce a new graph invariant \Lambda(G) that we call maxmaxflow, and put it in the context of some other well-known graph invariants, notably maximum degree and its relatives. We prove the equivalence of two "dual" definitions of maxmaxflow: one in terms of flows, the other in terms of cocycle bases. We then show how to bound the total number (or more generally, total weight) of various classes of subgraphs of G in terms of either maximum degree or maxmaxflow. We conclude with some conjectures concerning the relevance of maxmaxflow to the roots of chromatic polynomials.

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