Covers, orientations and factors

Péter Csikvári; András Imolay

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arXiv · 1905.06678

Covers, orientations and factors

Péter Csikvári·András Imolay

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Abstract

Given a graph $G$ with only even degrees let $\varepsilon(G)$ denote the number of Eulerian orientations, and let $h(G)$ denote the number of half graphs, that is, subgraphs $F$ such that $d_F(v)=d_G(v)/2$ for each vertex $v$. Recently, Borbényi and Csikvári proved that $\varepsilon(G)\geq h(G)$ holds true for all Eulerian graphs with equality if and and only if $G$ is bipartite. In this paper we give a simple new proof of this fact, and we give identities and inequalities for the number of Eulerian orientations and half graphs of a $2$-cover of a graph $G$.

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BibTeX RIS

Péter Csikvári, András Imolay. 2020-05-26. Covers, orientations and factors. https://arxiv.org/abs/1905.06678

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