A Note on $\{k,n-k\}$-Factors of Regular Graphs

Details A Note on $\{k,n-k\}$-Factors of Regular Graphs A Note on $\{k,n-k\}$-Factors of Regular Graphs

2011-12-04

arxiv.org/abs/1112.0748v1

Mathematics

Combinatorics

Scientific paper

Let $r$ be an odd integer, and $k$ an even integer. In this note, we present
$r$-regular graphs which have no $\{k,r-k\}$-factors for all $1\le k\le
{r\over2}-1$. This gives a negative answer to a problem posed by Akbari and
Kano recently.

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