Interlacement in 4-regular graphs: a new approach using nonsymmetric matrices
DOI:
https://doi.org/10.11575/cdm.v9i1.62166Abstract
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 $C^{\prime}$ are Euler systems of $F$ then $M(C,C^{\prime})$ and $M(C^{\prime},C)$ are inverses, and for any circuit partition $P$, $M(C^{\prime},P)=M(C^{\prime},C)\cdot M(C,P)$. This machinery allows for short proofs of several results regarding the linear algebra of interlacement.Downloads
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