A Result on Large Induced Subgraphs with Prescribed Residues in Bipartite Graphs
It was proved by Scott that for every $k\ge 2$, there exists a constant $c(k)>0$ such that for every bipartite $n$-vertex graph $G$ without isolated vertices, there exists an induced subgraph $H$ of order at least $c(k)n$ such that $\operatorname{deg}_H(v) \equiv 1\pmod{k}$ for each $v \in H$. Sc...
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Veröffentlicht in: | The Electronic journal of combinatorics 2023-01, Vol.30 (1) |
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Format: | Artikel |
Sprache: | eng |
Online-Zugang: | Volltext |
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Zusammenfassung: | It was proved by Scott that for every $k\ge 2$, there exists a constant $c(k)>0$ such that for every bipartite $n$-vertex graph $G$ without isolated vertices, there exists an induced subgraph $H$ of order at least $c(k)n$ such that $\operatorname{deg}_H(v) \equiv 1\pmod{k}$ for each $v \in H$. Scott conjectured that $c(k) = \Omega(1/k)$, which would be tight up to the multiplicative constant. We confirm this conjecture. |
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ISSN: | 1077-8926 1077-8926 |
DOI: | 10.37236/11454 |