On the independence number of sparse graphs

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Web18 de set. de 2024 · The independence number of a graph G, denoted by α (G), is the maximum cardinality of an independent set of vertices in G. [Henning and Löwenstein An …

On the Lovász Theta function for Independent Sets in Sparse Graphs

Web15 de jul. de 2024 · Wikipedia defines a graphical model as follows: A graphical model is a probabilistic model for which a graph denotes the conditional independence structure between random variables. They are commonly used in probability theory, statistics - particularly Bayesian statistics and machine learning. A supplementary view is that … 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 … tss nextcloud

Representation of short distances in structurally 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 … Web1 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 … Web1 de nov. de 2014 · Alon N (1996) Independence numbers of locally sparse graphs and a Ramsey type problem. Random Struct. Algorithm 9:271–278. Alon N, Spencer J (1992) The probabilistic method. tssn full form

Lower bounds for independence numbers of some locally sparse graphs

A note on the independence number of triangle-free graphs

Web26 de set. de 2012 · As the names indicate sparse graphs are sparsely connected (eg: Trees). Usually the number of edges is in O (n) where n is the number of vertices. Therefore adjacency lists are preferred since they require constant space for every edge. Dense graphs are densely connected. Here number of edges is usually O (n^2). WebIn 1943, Hadwiger conjectured that every graph with no Kt minor is (t−1)-colorable for every t≥1. In the 1980s, Kostochka and Thomason independently p… tss number for importWeb15 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 … tss new zealand

"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 … " - On the independence number of sparse graphs

On the independence number of sparse graphs

Sequential Algorithms and Independent Sets Discovering on Large Sparse …

Web22 de jul. de 2024 · The paper presents a simple, yet robust computer vision system for robot arm tracking with the use of RGB-D cameras. Tracking means to measure in real … 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,

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Web15 de nov. de 1993 · 1. Introduction A set of vertices of a graph is independent if the vertices are pairwise nonadjacent. The independence number of a graph G, a (G), is the cardinality of a largest independent set of G. For graph G= (V, E) and A s:- V we let the subgraph of G induced by A, G I A, be the graph with vertices A and edges being those … WebWe obtain new lower bounds for the independence number of K r -free graphs and linear k -uniform hypergraphs in terms of the degree sequence. This answers some old …

Web18 de abr. de 2015 · We consider the maximum independent set problem on graphs with maximum degree~. We show that the integrality gap of the Lovász -function based SDP is . This improves on the previous best result of , and almost matches the integrality gap of recently shown for stronger SDPs, namely those obtained using poly- levels of 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).

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 … 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 Theorem 1.1 is given below. We make no attempt to optimize the multiplicative constant here and in the rest of the paper.

Web28 de abr. de 2004 · The $b$-independence number $\a_b(G)$ is the size of the largest $b$-independent subset of $G$. When $b=1$ this reduces to the standard definition of independence number. We study this parameter in relation to the random graph …

WebCombinatorics, 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 tssn alphaWeb1 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 … tss numeroWeb15 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 … tssnt thinkificWeb7 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” … tss number irelandWeb1 de jan. de 1983 · Discrete Mathematics 46 (1983) 83-87 83 North,Holland A NOTE ON THE INDEPENDENCE NUMBER OF TRIANGLE-FREE GRAPHS James B. SHEARER Department of Mathematics, Umversity of Califor,zm, Berkeley, CA 94720, USA Received 26 February 1982 Revised 16 August 1982 Let G be a triangle-free graph on n points … tss ntWeb1 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 … t s snowWeb10 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. tss ntt