Remark on a paper of Lovász
Václav Chvátal (1968)
Commentationes Mathematicae Universitatis Carolinae
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Václav Chvátal (1968)
Commentationes Mathematicae Universitatis Carolinae
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Jaroslav Nešetřil, Vojtěch Rödl (1976)
Commentationes Mathematicae Universitatis Carolinae
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I.B. Lackovic, D.M. Cvetkovic (1976)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Jerzy Topp (1990)
Mathematica Slovaca
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Simić, Slobodan K. (1988)
Publications de l'Institut Mathématique. Nouvelle Série
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Vladislav Bína, Jiří Přibil (2015)
Commentationes Mathematicae Universitatis Carolinae
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The paper brings explicit formula for enumeration of vertex-labeled split graphs with given number of vertices. The authors derive this formula combinatorially using an auxiliary assertion concerning number of split graphs with given clique number. In conclusion authors discuss enumeration of vertex-labeled bipartite graphs, i.e., a graphical class defined in a similar manner to the class of split 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.