论文标题
$（2K+1）$的分解 - 包含特殊跨度$ 2K $的常规图 - 汇总的cayley图表到长度为$ 2K+1 $的路径
Decomposition of $(2k+1)$-regular graphs containing special spanning $2k$-regular Cayley graphs into paths of length $2k+1$
论文作者
论文摘要
图$ g $的$ p_ \ ell $ - 分组是一组$ g $中的$ \ ell $ edges的路径，覆盖了$ g $的边缘集。 Favaron，Genest和Kouider（2010）猜想，每个包含完美匹配的$（2K+1）$ - $ p_ {2k+1} $ - 分解。他们还以$ 5 $的规格图验证了这一猜想，而没有循环的$ 4 $。在2015年，博特勒，莫塔和瓦卡巴亚西以$ 5 $的规格图验证了这一猜想，没有三角形。在本文中，我们以$（2K+1）$ - 常规图的验证，其中包含$ k $ th的功率；并以$ 5 $的规范图，其中包含特殊跨度$ 4 $的cayley图形。
A $P_\ell$-decomposition of a graph $G$ is a set of paths with $\ell$ edges in $G$ that cover the edge set of $G$. Favaron, Genest, and Kouider (2010) conjectured that every $(2k+1)$-regular graph that contains a perfect matching admits a $P_{2k+1}$-decomposition. They also verified this conjecture for $5$-regular graphs without cycles of length $4$. In 2015, Botler, Mota, and Wakabayashi verified this conjecture for $5$-regular graphs without triangles. In this paper, we verify it for $(2k+1)$-regular graphs that contain the $k$th power of a spanning cycle; and for $5$-regular graphs that contain special spanning $4$-regular Cayley graphs.
