DISJOINT CYCLES WITH PRESCRIBED LENGTHS AND INDEPENDENT EDGES IN GRAPHS

Title & Authors
DISJOINT CYCLES WITH PRESCRIBED LENGTHS AND INDEPENDENT EDGES IN GRAPHS
Wang, Hong;

Abstract
We conjecture that if $\small{k{\geq}2}$ is an integer and G is a graph of order n with minimum degree at least (n+2k)/2, then for any k independent edges $\small{e_1}$, $\small{{\cdots}}$, $\small{e_k}$ in G and for any integer partition $\small{n=n_1+{\cdots}+n_k}$ with $\small{n_i{\geq}4(1{\leq}i{\leq}k)}$, G has k disjoint cycles $\small{C_1}$, $\small{{\cdots}}$, $\small{C_k}$ of orders $\small{n_1}$, $\small{{\cdots}}$, $\small{n_k}$, respectively, such that $\small{C_i}$ passes through $\small{e_i}$ for all $\small{1{\leq}i{\leq}k}$. We show that this conjecture is true for the case k = 2. The minimum degree condition is sharp in general.
Keywords
cycles;disjoint cycles;cycle coverings;
Language
English
Cited by
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