Eigenvalues and parity factors in graphs
| Autor: | Kim, Donggyu, O, Suil |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $G$ be a graph and let $g, f$ be nonnegative integer-valued functions defined on $V(G)$ such that $g(v) \le f(v)$ and $g(v) \equiv f(v) \pmod{2}$ for all $v \in V(G)$. A $(g,f)$-parity factor of $G$ is a spanning subgraph $H$ such that for each vertex $v \in V(G)$, $g(v) \le d_H(v) \le f(v)$ and $f(v)\equiv d_H(v) \pmod{2}$. We prove sharp upper bounds for certain eigenvalues in an $h$-edge-connected graph $G$ with given minimum degree to guarantee the existence of a $(g,f)$-parity factor; we provide graphs showing that the bounds are optimal. This result extends the recent one of the second author (2022), extending the one of Gu (2014), Lu (2010), Bollb{\'a}s, Saito, and Wormald (1985), and Gallai (1950). Comment: 16 pages, 1 figure |
| Databáze: | arXiv |
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