论文标题
汉密尔顿的线图分解
Hamilton decompositions of line graphs
论文作者
论文摘要
事实证明，如果图形是规则的，并且包含汉密尔顿周期，或者是奇数的规则，并包含汉密尔顿$ 3 $的$ 3 $因素，则其线路图是汉密尔顿可分解的。该结果部分扩展了Kotzig的结果，即当且仅当其线路图是汉密尔顿可解释的情况下，$ 3 $的图形是哈密顿量，并证明了Bermond的猜想表明，汉密尔顿可分解图的界限是汉密尔顿可分解的。
It is proved that if a graph is regular of even degree and contains a Hamilton cycle, or regular of odd degree and contains a Hamiltonian $3$-factor, then its line graph is Hamilton decomposable. This result partially extends Kotzig's result that a $3$-regular graph is Hamiltonian if and only if its line graph is Hamilton decomposable, and proves the conjecture of Bermond that the line graph of a Hamilton decomposable graph is Hamilton decomposable.
