Results 21 to 30 of about 215 (116)
Discussiones Mathematicae Graph Theory, 2001 Summary: A dominating set \(D\) for a graph \(G\) is a subset of \(V(G)\) such that any vertex in \(V(G)-D\) has a neighbor in \(D\), and a domination number \(\gamma(G)\) is the size of a minimum dominating set for \(G\). For the Cartesian product \(G\square H\) Vizing's conjecture [cf. \textit{V. G. Vizing}, Vychisl.
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An Algebraic Exploration of Dominating Sets and Vizing's Conjecture [PDF]
The Electronic Journal of Combinatorics, 2012 Systems of polynomial equations are commonly used to model combinatorial problems such as independent set, graph coloring, Hamiltonian path, and others. We formulate the dominating set problem as a system of polynomial equations in two different ways: first, as a single, high-degree polynomial, and second as a collection of polynomials based on the ...
Margulies, S., Hicks, I.V.
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, 2017 Vizing conjectured that G is a simple and ∆-critical graph with m edges then . In this paper we prove the conjecture for graphs with and .
M. Santhi, P. Anitha
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An improvement in the two-packing bound related to Vizing\u27s conjecture [PDF]
, 2020 Vizing\u27s conjecture states that the domination number of the Cartesian product of graphs is at least the product of the domination numbers of the two factor graphs.
Wolff, Kimber
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The chromatic index of simple graphs [PDF]
, 1975 The object of this thesis is twofold: (i) to study the structural properties of graphs which are critical with respect to edge-colourings; (ii) to apply the results obtained to the classification problem arising from Vizing's Theorem.
Fiorini, S
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Behzad-Vizing conjecture and Cartesian product graphs
Electronic Notes in Discrete Mathematics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zmazek, Blaž, Žerovnik, Janez
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On the domination number of the cartesian product of the path graph and any pair of graphs [PDF]
, 2023 It is known that for any graph $G,$ $\gamma (G\square P_2)\geq \gamma (G)$ where $\gamma$ stands for the domination number, $\square$ for the cartesian product and $P_2$ is the path graph on two vertices. In an attempt to prove Vizing's conjecture, Clark
Tout, Omar
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On Strongly and Robustly Critical Graphs
Journal of Graph Theory, EarlyView.ABSTRACT In extremal combinatorics, it is common to focus on structures that are minimal with respect to a certain property. In particular, critical and list‐critical graphs occupy a prominent place in graph coloring theory. Stiebitz, Tuza, and Voigt introduced strongly critical graphs, i.e., graphs that are k $k$‐critical yet L $L$‐colorable with ...
Anton Bernshteyn +3 more
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Extremal Colorings and Independent Sets [PDF]
, 2018 We consider several extremal problems of maximizing the number of colorings and independent sets in some graph families with fixed chromatic number and order.
Engbers, John, Erey, Aysel
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Journal of Personality, EarlyView.ABSTRACT Objectives Counter‐empathy involves responding to others' assumed emotions incongruently. Research on dispositional counter‐empathy predominantly focuses on specific counter‐empathic constructs without clearly mapping its cardinal dimensions.
Jake R. Siamro, Christian H. Jordan
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