Polyhedral graph abstractions and an approach to the Linear Hirsch Conjecture

Details Polyhedral graph abstractions and an approach to the Linear Hirsch Conjecture Polyhedral graph abstractions and an approach to the Linear Hirsch Conjecture

2011-03-17

arxiv.org/abs/1103.3362v1

Mathematics

Combinatorics

18 pages, 4 figures

Scientific paper

We introduce a new combinatorial abstraction for the graphs of polyhedra. The new abstraction is a flexible framework defined by combinatorial properties, with each collection of properties taken providing a variant for studying the diameters of polyhedral graphs. One particular variant has a diameter which satisfies the best known upper bound on the diameters of polyhedra. Another variant has superlinear asymptotic diameter, and together with some combinatorial operations, gives a concrete approach for disproving the Linear Hirsch Conjecture.

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