Interlacement in 4-regular graphs: a new approach using nonsymmetric matrices

Details Interlacement in 4-regular graphs: a new approach using nonsymmetric matrices Interlacement in 4-regular graphs: a new approach using nonsymmetric matrices

2012-04-02

arxiv.org/abs/1204.0482v2

Mathematics

Combinatorics

v1: 15 pages, 6 figures v2: minor corrections

Scientific paper

Let F be a 4-regular graph with an Euler system C. We introduce a simple way to modify the interlacement matrix of C so that every circuit partition P of F has an associated modified interlacement matrix M(P,C). If C and C' are Euler systems of F then M(C,C') and M(C',C) are inverses, and for any circuit partition P, M(P,C') is M(C,C') times M(P,C). This machinery allows for short proofs of several results regarding the linear algebra of interlacement.

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