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arXiv · 2203.05326

Arc coloring of odd graphs for hamiltonicity

Italo J. Dejter
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Abstract

Coloring the arcs of biregular graphs was introduced with possible applications to industrial chemistry, molecular biology, cellular neuroscience, etc. Here, we deal with arc coloring in some non-bipartite graphs. In fact, for $1<k\in\mathbb{Z}$, we find that the odd graph $O_k$ has an arc factorization with colors $0,1,\ldots,k$ such that the sum of colors of the two arcs of each edge equals $k$. This is applied to analyzing the influence of such arc factorizations in recently constructed uniform 2-factors in $O_k$ and in Hamilton cycles in $O_k$ as well as in its double covering graph known as the middle-levels graph $M_k$.

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Italo J. Dejter. 2022-03-10. Arc coloring of odd graphs for hamiltonicity. https://arxiv.org/abs/2203.05326

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