Cycle Partitions in Dense Regular Digraphs and Oriented Graphs
A conjecture of Jackson from 1981 states that every d-regular oriented graph on n vertices with $n\leq 4d+1$ is Hamiltonian. We prove this conjecture for sufficiently large n. In fact we prove a more general result that for all $\alpha>0$ , there exists $n_0=n_0(\alpha )$ such...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425000283/type/journal_article |
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| Summary: | A conjecture of Jackson from 1981 states that every d-regular oriented graph on n vertices with
$n\leq 4d+1$
is Hamiltonian. We prove this conjecture for sufficiently large n. In fact we prove a more general result that for all
$\alpha>0$
, there exists
$n_0=n_0(\alpha )$
such that every d-regular digraph on
$n\geq n_0$
vertices with
$d \ge \alpha n $
can be covered by at most
$n/(d+1)$
vertex-disjoint cycles, and moreover that if G is an oriented graph, then at most
$n/(2d+1)$
cycles suffice. |
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| ISSN: | 2050-5094 |