A small trivalent graph of girth 14.
Exoo, Geoffrey (2002)
The Electronic Journal of Combinatorics [electronic only]
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Exoo, Geoffrey (2002)
The Electronic Journal of Combinatorics [electronic only]
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Marián Sudolský (1978)
Mathematica Slovaca
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Pavol Híc (1992)
Mathematica Slovaca
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Walter Carballosa, Ruy Fabila-Monroy, Jesús Leaños, Luis Manuel Rivera (2017)
Discussiones Mathematicae Graph Theory
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Let G = (V, E) be a graph of order n and let 1 ≤ k < n be an integer. The k-token graph of G is the graph whose vertices are all the k-subsets of V, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. In this paper we characterize precisely, for each value of k, which graphs have a regular k-token graph and which connected graphs have a planar k-token graph.
Hegde, Suresh Manjanath, Shetty, Sudhakar (2006)
Applied Mathematics E-Notes [electronic only]
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André Bouchet (1999)
Annales de l'institut Fourier
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The following result is proved: if a bipartite graph is not a circle graph, then its complement is not a circle graph. The proof uses Naji’s characterization of circle graphs by means of a linear system of equations with unknowns in . At the end of this short note I briefly recall the work of François Jaeger on circle graphs.
Boštjan Brešar, Manoj Changat, Ajitha R. Subhamathi, Aleksandra Tepeh (2010)
Discussiones Mathematicae Graph Theory
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The periphery graph of a median graph is the intersection graph of its peripheral subgraphs. We show that every graph without a universal vertex can be realized as the periphery graph of a median graph. We characterize those median graphs whose periphery graph is the join of two graphs and show that they are precisely Cartesian products of median graphs. Path-like median graphs are introduced as the graphs whose periphery graph has independence number 2, and it is proved that there are...
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.