Displaying similar documents to “Remarks on regular factors of regular graphs”

Splitting Cubic Circle Graphs

Lorenzo Traldi (2016)

Discussiones Mathematicae Graph Theory

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We show that every 3-regular circle graph has at least two pairs of twin vertices; consequently no such graph is prime with respect to the split decomposition. We also deduce that up to isomorphism, K4 and K3,3 are the only 3-connected, 3-regular circle graphs.

The Existence Of P≥3-Factor Covered Graphs

Sizhong Zhou, Jiancheng Wu, Tao Zhang (2017)

Discussiones Mathematicae Graph Theory

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A spanning subgraph F of a graph G is called a P≥3-factor of G if every component of F is a path of order at least 3. A graph G is called a P≥3-factor covered graph if G has a P≥3-factor including e for any e ∈ E(G). In this paper, we obtain three sufficient conditions for graphs to be P≥3-factor covered graphs. Furthermore, it is shown that the results are sharp.