New Results on $k$-Independence of Graphs
نویسندگان
چکیده
منابع مشابه
New 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 کاملK-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 کاملNew results on upper domatic number of graphs
For a graph $G = (V, E)$, a partition $pi = {V_1,$ $V_2,$ $ldots,$ $V_k}$ of the vertex set $V$ is an textit{upper domatic partition} if $V_i$ dominates $V_j$ or $V_j$ dominates $V_i$ or both for every $V_i, V_j in pi$, whenever $i neq j$. The textit{upper domatic number} $D(G)$ is the maximum order of an upper domatic partition. We study the properties of upper domatic number and propose an up...
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 k-independence in graphs with emphasis on trees
In a graphG= (V ,E) of order n and maximum degree , a subset S of vertices is a k-independent set if the subgraph induced by S has maximum degree less or equal to k − 1. The lower k-independence number ik (G) is the minimum cardinality of a maximal k-independent set in G and the k-independence number k(G) is the maximum cardinality of a k-independent set. We show that ik n − + k − 1 for any gra...
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 Electronic Journal of Combinatorics
سال: 2017
ISSN: 1077-8926
DOI: 10.37236/5730