A Simple Proof of the Perfect Matching Theorem
Ján Plesník (1975)
Matematický časopis
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Ján Plesník (1975)
Matematický časopis
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Petrović, Miroslav (1991)
Publications de l'Institut Mathématique. Nouvelle Série
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Marta Borowiecka-Olszewska, Ewa Drgas-Burchardt (2017)
Discussiones Mathematicae Graph Theory
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A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose...
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.
Cvetkovic, Dragos M. (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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I.B. Lackovic, D.M. Cvetkovic (1976)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Slobodan K. Simić (1980)
Publications de l'Institut Mathématique
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Liu, Guizhen, Qian, Jianbo, Sun, Jonathan Z., Xu, Rui (2008)
International Journal of Mathematics and Mathematical Sciences
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Anna Benini, Anita Pasotti (2015)
Discussiones Mathematicae Graph Theory
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An α-labeling of a bipartite graph Γ of size e is an injective function f : V (Γ) → {0, 1, 2, . . . , e} such that {|ƒ(x) − ƒ(y)| : [x, y] ∈ E(Γ)} = {1, 2, . . . , e} and with the property that its maximum value on one of the two bipartite sets does not reach its minimum on the other one. We prove that the generalized Petersen graph PSn,3 admits an α-labeling for any integer n ≥ 1 confirming that the conjecture posed by Vietri in [10] is true. In such a way we obtain an infinite class...
Hoang, C.T., Le, V.B. (2001)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Amanda Niedzialomski (2016)
Discussiones Mathematicae Graph Theory
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For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G) → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u) − f(v)| ≥ k + 1 − d(u, v). We consider k-radio labelings of G when k = diam(G). In this setting, f is injective; if f is also surjective onto {1, 2, . . . , |V (G)|}, then f is a consecutive radio labeling. Graphs that can be labeled with such a labeling are called radio graceful. In this paper, we give two results on the existence of radio...
Gábor Bacsó, Danuta Michalak, Zsolt Tuza (2005)
Discussiones Mathematicae Graph Theory
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A graph G is hereditarily dominated by a class 𝓓 of connected graphs if each connected induced subgraph of G contains a dominating induced subgraph belonging to 𝓓. In this paper we characterize graphs hereditarily dominated by classes of complete bipartite graphs, stars, connected bipartite graphs, and complete k-partite graphs.