On the independence number of sparse graphs

Author: tmdq

August undefined, 2024

WebHowever, computing the independence number of a given graph is well-known to be an NP-hard problem. Our main focus here is thus nding e cient methods to compute (up to vanishing errors) the independence number of large sparse random graphs. Building on recent resultsBermolen et al.(2024a),Brightwell Webtitle = "Independence numbers of locally sparse graphs and a Ramsey type problem", abstract = "Let G = (V,E) be a graph on n vertices with average degree t ≥ 1 in …

What is the distinction between sparse and dense graphs?

WebOur proof technique is an extension of a method of Caro [New Results on the Independence Number, Technical report, Tel Aviv University, 1979] and Wei [A Lower Bound on the Stability Number of a Simple Graph, TM 81-11217-9, Bell Laboratories, Berkley Heights, NJ, 1981], and we also give a new short proof of the main result of Caro … WebCombinatorics, Probability and Computing. Periodical Home; Latest Issue; Archive; Authors; Affiliations; Home; Browse by Title; Periodicals; Combinatorics ... citi bank savings and cds

Independent sets - Graph Theory - SageMath

Web1 de mai. de 2004 · in this paper that this is true for the b-independence n umber. Theorem 1 L et b b e a p osit i v e in te ger c onstan t and let ǫ > 0 b e giv en. Assume that d 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 … 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) ... citibank savings rate history

Sparse Pseudo-Random Graphs are Hamiltonian - ETH Z

On the number of types in sparse graphs

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 … 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. diaper rash diarrhea toddlerWebLet G = (V, E) be a graph on n vertices with average degree t ≥ 1 in which for every vertex v ϵ V the induced subgraph on the set of all neighbors of v is r-colorable.We show that the independence number of G is at least log t, for some absolute positive constant c.This strengthens a well-known result of Ajtai, Komlós, and Szemerédi [1]. Combining their … citi bank savings connect

"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. … " - On the independence number of sparse graphs

On the independence number of sparse graphs

Independence numbers of locally sparse graphs and a Ramsey …

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 … 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-

Did you know?

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, 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” …

Web15 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 … 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 ...

WebOne simple and efficient way to precompute this table is by observing that one interval whose length is a power of 2 can be split into 2 smaller intervals. This observation translates into the following recurrence relation: r m q [ h] [ i] = m i n ( r m q [ h − 1] [ i], r m q [ h − 1] [ i + 2 h − 1]) . Below is an example of one such ... 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.

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.

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 … citibank savings high yieldWebsparse pseudo-random graphs. It should be stressed that the deﬁnition of pseudo-random graphs used in this study is rather restrictive and applies only to regular graphs. It seems plausible, however, that our techniques can be used to prove Hamiltonicity of almost regular graphs (i.e., graphs in which all degrees are very close to an average ... diaper rash elecareWeb22 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 time the robot state given by three angles and with known restrictions about the robot geometry. The tracking system consists of two parts: image preprocessing and machine learning. In … diaper rash due to food allergyWebThe 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 … diaper rash during teethingWeb18 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 … diaper rash exam findingsWebIn 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… diaper rashes in adultsWebLet G = (V, E) be a graph on n vertices with average degree t ≥ 1 in which for every vertex v ϵ V the induced subgraph on the set of all neighbors of v is r-colorable.We show that the … diaper rash examples