arXiv subjects

Farid Bouya

Publications and source records attributed to Farid Bouya.

2 recordsLinked to original sources

arXiv2020

A Highly Symmetric Hamilton Decomposition for Hypercubes

A Hamilton decomposition of a graph is a partitioning of its edge set into disjoint spanning cycles. The existence of such decompositions is known for all hypercubes of even dimension $2n$. We give a decomposition for the case $n = 2^a3^b$ that is highly symmetric in the sense that every cycle can be derived from every other cycle just by permuting the axes. We conjecture that a similar decomposition exists for every n.

math.CO↗

arXiv2019

Seymour's second-neighborhood conjecture from a different perspective

Seymour's Second-Neighborhood Conjecture states that every directed graph whose underlying graph is simple has at least one vertex $v$ such that the number of vertices of out-distance $2$ from $v$ is at least as large as the number of vertices of out-distance $1$ from it. We present alternative statements of the conjecture in the language of linear algebra.

math.CO↗