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Large Independent Sets on Random d-Regular Graphs with Fixed Degree d
Computation, 2023 The maximum independent set problem is a classic and fundamental combinatorial challenge, where the objective is to find the largest subset of vertices in a graph such that no two vertices are adjacent.
Raffaele Marino, Scott Kirkpatrick
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Independent Sets in Polarity Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2016 Given a projective plane $ $ and a polarity $ $ of $ $, the corresponding polarity graph is the graph whose vertices are the points of $ $, and two distinct points $p_1$ and $p_2$ are adjacent if $p_1$ is incident to $p_2^{ }$ in $ $. A well-known example of a polarity graph is the Erd s-R nyi orthogonal polarity graph $ER_q$, which appears ...
Tait, Michael, Timmons, Craig
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Independent Sets In Association Schemes [PDF]
Combinatorica, 2006 15 pages; This is the corrected version that will appear in ...
Godsil, C. D., Newman, M. W.
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Algorithmic Aspects of Some Variants of Domination in Graphs
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 A set S ⊆ V is a dominating set in G if for every u ∈ V \ S, there exists v ∈ S such that (u, v) ∈ E, i.e., N[S] = V . A dominating set S is an isolate dominating set (IDS) if the induced subgraph G[S] has at least one isolated vertex.
Kumar J. Pavan, Reddy P.Venkata Subba
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SGR 1806-20 Is a Set of Independent Relaxation Systems [PDF]
, 1999 The Soft Gamma Repeater 1806-20 produced patterns of bursts during its 1983 outburst that indicate multiple independent energy accumulation sites, each driven by a continuous power source, with sudden, incomplete releases of the accumulated energy.
David M. Palmer +3 more
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Discrete Applied Mathematics, 2016 The regular independence number, introduced by Albertson and Boutin in 1990, is the size of a largest set of independent vertices with the same degree. Lower bounds were proven for this invariant, in terms of the order, for trees and planar graphs.
Yair Caro, Adriana Hansberg, Ryan Pepper
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Independent sets in algebraic hypergraphs
Journal of the European Mathematical Society, 2021 In this paper we study hypergraphs definable in an algebraically closed field. Our goal is to show, in the spirit of the so-called transference principles in extremal combinatorics, that if a given algebraic hypergraph is “dense” in a certain sense, then a generic low-dimensional subset of its vertices induces a subhypergraph that is also “dense.” (For
Anton Bernshteyn +2 more
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On the number of maximum independent sets of graphs [PDF]
Transactions on Combinatorics, 2014 Let $G$ be a simple graph. An independent set is a set of pairwise non-adjacent vertices. The number of vertices in a maximum independent set of $G$ is denoted by $alpha(G)$. In this paper, we characterize graphs $G$ with $n$ vertices and with maximum
Tajedin Derikvand, Mohammad Reza Oboudi
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Fair Representation by Independent Sets [PDF]
, 2017 For a hypergraph $H$ let $ (H)$ denote the minimal number of edges from $H$ covering $V(H)$. An edge $S$ of $H$ is said to represent {\em fairly} (resp. {\em almost fairly}) a partition $(V_1,V_2, \ldots, V_m)$ of $V(H)$ if $|S\cap V_i|\ge \lfloor\frac{|V_i|}{ (H)}\rfloor$ (resp. $|S\cap V_i|\ge \lfloor\frac{|V_i|}{ (H)}\rfloor-1$) for all $i \le m$.
Aharoni, Ron +6 more
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Weighted Domination of Independent Sets [PDF]
Graphs and Combinatorics, 2019 The {\em independent domination number} $ ^i(G)$ of a graph $G$ is the maximum, over all independent sets $I$, of the minimal number of vertices needed to dominate $I$. It is known \cite{abz} that in chordal graphs $ ^i$ is equal to $ $, the ordinary domination number.
Aharoni, Ron, Gorelik, Irina
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