Interlacement in 4-regular graphs: a new approach using nonsymmetric matrices
Combinatorics
2015-04-20 v3
Abstract
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(C,P). 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(C',P)=M(C',C)M(C,P). This machinery allows for short proofs of several results regarding the linear algebra of interlacement.
Cite
@article{arxiv.1204.0482,
title = {Interlacement in 4-regular graphs: a new approach using nonsymmetric matrices},
author = {Lorenzo Traldi},
journal= {arXiv preprint arXiv:1204.0482},
year = {2015}
}
Comments
v1: 15 pages, 6 figures v2: minor corrections v3: 14 pages, 4 figures. Examples have been replaced with a more detailed discussion of relationship with earlier results