On the independence number of sparse graphs
WebLet 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 … WebLet 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 …
On the independence number of sparse graphs
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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 … 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.
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 ...
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 … 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).
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 Mathematics, Carnegie Mellon University, Pittsburgh, USA Received September 1, 1987 Revised June 1, 1988 Let a(GP) denote the independence number of the random …
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” … incline press works what muscleWeb2 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 … inbuilt stack in cWebT1 - 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. inbuilt stack in c++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 … inbuilt stack in cppWebproperties), 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 ... incline property management nvWeb1 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 … inbuilt stack in pythonWeb1 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 inbuilt stabilizer in ac suppliers