The k-independence number of graph products
نویسندگان
چکیده
منابع مشابه
New Approach to the k-Independence Number of a Graph
Let G = (V,E) be a graph and k > 0 an integer. A k-independent set S ⊆ V is a set of vertices such that the maximum degree in the graph induced by S is at most k. With αk(G) we denote the maximum cardinality of a k-independent set of G. We prove that, for a graph G on n vertices and average degree d, αk(G) > k+1 ⌈d⌉+k+1n, improving the hitherto best general lower bound due to Caro and Tuza [Imp...
متن کاملSpectral bounds for the k-independence number of a graph
In this paper, we obtain two spectral upper bounds for the k-independence number of a graph which is is the maximum size of a set of vertices at pairwise distance greater than k. We construct graphs that attain equality for our first bound and show that our second bound compares favorably to previous bounds on the k-independence number.
متن کاملOn the chromatic number and independence number of hypergraph products
The hypergraph product G2H has vertex set V (G) × V (H), and edge set {e × f : e ∈ E(G), f ∈ E(H)}, where × denotes the usual cartesian product of sets. We construct a hypergraph sequence {Gn} for with χ(Gn) → ∞ and χ(Gn2Gn) = 2 for all n. This disproves a conjecture of Berge and Simonovits [2]. On the other hand, we show that if G and H are hypergraphs with infinite chromatic number, then the ...
متن کاملOn the k-independence number in graphs
For an integer k ≥ 1 and a graph G = (V,E), a subset S of V is kindependent if every vertex in S has at most k − 1 neighbors in S. The k-independent number βk(G) is the maximum cardinality of a kindependent set of G. In this work, we study relations between βk(G), βj(G) and the domination number γ(G) in a graph G where 1 ≤ j < k. Also we give some characterizations of extremal graphs.
متن کاملOn the Independence Number of the Generalized Petersen Graph P(n,k)∗
Let G = (V (G),E(G)) be a simple finite undirected graph. A set S ⊆ V (G) is an independent set if no two vertices of S are adjacent. The independence number α(G) is the maximum cardinality of an independent set in G. In this paper, we investigate the independence number of generalized Petersen graph, and give the exact values of P(n,k) for k = 1,2,3,5.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Art of Discrete and Applied Mathematics
سال: 2017
ISSN: 2590-9770
DOI: 10.26493/2590-9770.1216.6d2