Optimal Graphs for Independence and k-Independence Polynomials
نویسندگان
چکیده
منابع مشابه
K-independence Critical Graphs
Let k be a positive integer and G = (V (G), E(G)) a graph. A subset S of V (G) is a k-independent set of G if the subgraph induced by the vertices of S has maximum degree at most k − 1. The maximum cardinality of a k-independent set of G is the k-independence number βk(G). In this paper, we study the properties of graphs for which the k-independence number changes whenever an edge or vertex is ...
متن کاملApproximating independence polynomials of claw-free graphs
Matchings in graphs correspond to independent sets in the corresponding line graphs. Line graphs are an important subclass of claw-free graphs. Hence studying independence polynomials of claw-free graphs is a natural extension of studying matching polynomials of graphs. We extend a result of Bayati et.al. showing a fully polynomial time approximation scheme (FPTAS) for computing the independenc...
متن کاملNew Results on k-Independence of Graphs
Let G = (V,E) be a graph and k > 0 an integer. A k-independent set S ⊆ G is a set of vertices such that the maximum degree in the graph induced by S is at most k. Denote by αk(G) the maximum cardinality of a k-independent set of G. For a graph G on n vertices and average degree d, Turán’s theorem asserts that α0(G) > n d+1 , where the equality holds if and only if G is a union of cliques of equ...
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 کاملK-independence Stable Graphs upon Edge Removal
Let k be a positive integer and G = (V (G), E(G)) a graph. A subset S of V (G) is a k-independent set of G if the subgraph induced by the vertices of S has maximum degree at most k−1. The maximum cardinality of a k-independent set of G is the k-independence number βk(G). A graph G is called β − k -stable if βk(G − e) = βk(G) for every edge e of E(G). First we give a necessary and sufficient con...
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: Graphs and Combinatorics
سال: 2018
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-018-1946-0