On the independence number of sparse graphs

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August undefined, 2024

Web10 de abr. de 2024 · In this section, we consider the ratio-k-cuts of sparse graphs and prove Theorem 2. Note that a set of vertices in a graph G is independent if no two vertices from this set are joined by an edge. The independence number \(\alpha (G)\) is the maximum number of vertices in an independent set of G. Web2 Locally sparse graphs Let (G) denote the independence number of G, that is, the maximum number of vertices in an independent set in G. The main step in the proof of …

Bounds on Half Graph Orders in Powers of Sparse Graphs

Web23 de dez. de 2024 · Abstract The k-independence number of a graph, αk(G), is the maximum size of a set of vertices at pairwise distance greater than k, or alternatively, the … Web8 de abr. de 2014 · 2 Answers. Generally, it is said that a graph with n vertices is dense if it has Theta ( n ^2) edges and is sparse otherwise. This means that a graph is dense if the average degree of each vertex is lineal, and sparse if sublineal. Sparsity does not deppend on size. For instance, trees are sparse (because a tree with n nodes has n-1 edges). cigar box chord chart

On the Lovász Theta function for Independent Sets in Sparse Graphs

Web1 de mai. de 2024 · We prove that every graph G of maximum degree at most 3 satisfies 3 2α(G)+α ' (G)+1 2t(G)≥n(G), where α(G) is the independence number of G,α ' (G) is the … Web23 de fev. de 2011 · Abstract. We obtain new lower bounds for the independence number of K-r-free graphs and linear k-uniform hypergraphs in terms of the degree sequence. … Webbound on the independence number of Kr-free graphs for large values of r. We also show how to obtain an algorithmic version of the above-mentioned SA+-based integrality gap result, via a coloring algorithm of Johansson. The resulting approximation guarantee of Oe(d/log2d) matches the best unique-games-based hardness result up to lower- dhcp read only

Independence numbers of locally sparse graphs and a Ramsey …

Sensors Free Full-Text Comparison of Graph Fitting and Sparse …

Webproperties), by low tree-depth colorings [26], by generalized coloring numbers [37], by sparse neighborhood covers [17, 18], by a game called the splitter game [18], and by the model-theoretic concepts of stability and independence [1]. For a broader discussion on graph theoretic sparsity we refer to the book of Ne set ril and Ossona de Mendez ... WebThe independence number of a graph is equal to the largest exponent in the graph's independence polynomial. The lower independence number may be similarly defined … cigar box chile cabernetWebCombinatorics, Probability and Computing (2004) 13, 295–309. c 2004 Cambridge University Press DOI: 10.1017/S0963548304006108 Printed in the United Kingdom On … dhcp relay fortinet

"WebThe (upper) vertex independence number of a graph, often called simply "the" independence number, is the cardinality of the largest independent vertex set, i.e., the size of a maximum independent vertex set (which is the same as the size of a largest maximal independent vertex set). The independence number is most commonly denoted … " - On the independence number of sparse graphs

On the independence number of sparse graphs

On the k-independence number of graphs - ScienceDirect

Web9 de mai. de 2024 · Bounded Clique Cover of Some Sparse Graphs. June 2016. ... (On the independence number of a graph in terms of order and size, {\it Discrete Math.} {\bf 232} (2001), 131-138) ... Web1 de abr. de 2024 · The power graph Γ G of a finite group G is the graph whose vertex set is G, two distinct elements being adjacent if one is a power of the other.In this paper, we …

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Web"The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers," Journal of Combinatorial Optimization, Springer, vol. 7(4), pages 353-359, December. … Web7 de abr. de 2024 · Nowhere dense graph classes, introduced by Nešetřil and Ossona de Mendez [2010, 2011], form a large variety of classes of “sparse graphs” …

Webindependence number. Acknowledgments I would like to thank Abhiruk Lahiri and Ben Moore for useful discussions of the subject. ... [14] M. Pilipczuk, S. Siebertz, and S. Toru´nczyk , On the number of types in sparse graphs, in Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS’18, ACM, 2024, WebT1 - Independence numbers of locally sparse graphs and a Ramsey type problem. AU - Alon, Noga Mordechai. PY - 1996/1/1. Y1 - 1996/1/1. N2 - Let G = (V,E) be a graph on n vertices with average degree t ≥ 1 in which for every vertex v E V the induced subgraph on the set of all neighbors of v is r-colorable.

Web14 de jun. de 2015 · On the independence number of sparse graphs. Random Struct. Algorithms, 7(3):269--272, 1995. Google Scholar Digital Library; V. Vu. A general upper bound on the list chromatic number of locally sparse graphs. Combinatorics Probability and Computing, 11(1):103--111, 2002. WebTheminimum-degree greedy algorithm, or Greedy for short, is a simple and well-studied method for finding independent sets in graphs. We show that it achieves a performance ratio of (Δ+2)/3 for approximating independent sets in graphs with degree bounded by Δ. The analysis yields a precise characterization of the size of the independent sets found …

Web1 de out. de 2024 · This paper generalizes and unifies the existing spectral bounds on the k-independence number of a graph, which is the maximum size of a set of vertices at …

Web7 de abr. de 2024 · Nowhere dense graph classes, introduced by Nešetřil and Ossona de Mendez [2010, 2011], form a large variety of classes of “sparse graphs” including the class of planar graphs, actually ... cigar box collection cigar box buildWeb1 de out. de 1995 · Lower bounds and approximation algorithms for the independence number α(G) in k-clique-free graphs G are studied and it is shown that there exists an … cigar box clock how to makeWeb1 de out. de 1996 · Let G = (V,E) be a graph on n vertices with average degree t ≥ 1 in which for every vertex v ∈ V the induced subgraph on the set of all neighbors of v is r … cigar box collectionsWeb1 de out. de 1995 · On the independence number of sparse graphs On the independence number of sparse graphs Shearer, James B. 1995-10-01 00:00:00 … dhcp relay gpon oltWebCombinatorics, Probability and Computing (2004) 13, 295–309. c 2004 Cambridge University Press DOI: 10.1017/S0963548304006108 Printed in the United Kingdom On the b-Independence cigar box cowesWeb15 de abr. de 1990 · Discrete Mathematics 81 (1990) 171-175 171 North-Holland ON THE INDEPENDENCE NUMBER OF RANDOM GRAPHS A.M. FRIEZE Department of Mathematics, Carnegie Mellon University, Pittsburgh, USA Received September 1, 1987 Revised June 1, 1988 Let a(GP) denote the independence number of the random … dhcp relay gns3