Results 31 to 40 of about 17,750 (263)
Note on robust coloring of planar graphs [PDF]
Opuscula MathematicaWe consider the robust chromatic number \(\chi_1(G)\) of planar graphs \(G\) and show that there exists an infinite family of planar graphs \(G\) with \(\chi_1(G) = 3\), thus solving a recent problem of Bacsó et al.
František Kardoš +2 more
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On P-transitive graphs and applications [PDF]
Electronic Proceedings in Theoretical Computer Science, 2011 We introduce a new class of graphs which we call P-transitive graphs, lying between transitive and 3-transitive graphs. First we show that the analogue of de Jongh-Sambin Theorem is false for wellfounded P-transitive graphs; then we show that the mu ...
Giacomo Lenzi
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On the Turán Properties of Infinite Graphs [PDF]
The Electronic Journal of Combinatorics, 2008 Let $G^{(\infty)}$ be an infinite graph with the vertex set corresponding to the set of positive integers ${\Bbb N}$. Denote by $G^{(l)}$ a subgraph of $G^{(\infty)}$ which is spanned by the vertices $\{1,\dots,l\}$. As a possible extension of Turán's theorem to infinite graphs, in this paper we will examine how large $\liminf_{l\rightarrow \infty} {|
Andrzej Dudek, Vojtech Rödl
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Classes of graphs with restricted interval models [PDF]
Discrete Mathematics & Theoretical Computer Science, 1999 We introduce q-proper interval graphs as interval graphs with interval models in which no interval is properly contained in more than q other intervals, and also provide a forbidden induced subgraph characterization of this class of graphs.
Andrzej Proskurowski, Jan Arne Telle
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The center of an infinite graph
Discrete Mathematics, 1996 In this note we extend the notion of the center of a graph to infinite graphs. Thus, a vertex is in the center of the infinite graph G if it is in the center of an increasing family of finite subgraphs covering G. We give different characterizations of when a vertex is in the center of an infinite graph and we prove that any infinite graph with at ...
Boza Prieto, Luis +2 more
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Infinite friendship graphs with infinite parameters
Journal of Combinatorial Theory, Series B, 1991 We study infinite graphs in which every set of \(\kappa\) vertices has exactly \(\lambda\) common neighbours. We prove that there exist \(2^{\sigma}\) such graphs of each infinite order \(\sigma\) if \(\kappa\) is finite and that for \(\kappa\) infinite there are \(2^{\lambda}\) of them of order \(\lambda\) and none of cardinality greater than ...
Gena Hahn +2 more
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Discussiones Mathematicae Graph Theory, 2013 The infimum of the least eigenvalues of all finite induced subgraphs of an infinite graph is defined to be its least eigenvalue. In [P.J. Cameron, J.M. Goethals, J.J. Seidel and E.E. Shult, Line graphs, root systems, and elliptic geometry, J. Algebra 43 (
Vijayakumar Gurusamy Rengasamy
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A sampling theory for infinite weighted graphs [PDF]
Opuscula Mathematica, 2011 We prove two sampling theorems for infinite (countable discrete) weighted graphs \(G\); one example being "large grids of resistors" i.e., networks and systems of resistors.
Palle E. T. Jorgensen
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Eternal domination and clique covering
Electronic Journal of Graph Theory and Applications, 2022 We study the relationship between the eternal domination number of a graph and its clique cove-ring number using both large-scale computation and analytic methods. In doing so, we answer two open questions of Klostermeyer and Mynhardt.
Gary MacGillivray +2 more
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Journal of Combinatorial Theory, Series B, 1988 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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