Blocking total dominating sets via edge contractions

نویسندگان

چکیده

Abstract In this paper, we study the problem of deciding whether total domination number a given graph G can be reduced using exactly one edge contraction (called 1 -Edge Contraction( ? t ) ). We focus on several classes and determine computational complexity problem. By putting together these results, manage to obtain complete dichotomy for H-free graphs.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Efficient Dominating and Edge Dominating Sets for Graphs and Hypergraphs

Let G = (V,E) be a graph. A vertex dominates itself and all its neighbors, i.e., every vertex v ∈ V dominates its closed neighborhood N [v]. A vertex set D in G is an efficient dominating (e.d.) set for G if for every vertex v ∈ V , there is exactly one d ∈ D dominating v. An edge set M ⊆ E is an efficient edge dominating (e.e.d.) set for G if it is an efficient dominating set in the line graph...

متن کامل

Edge dominating sets and vertex covers

Bipartite graphs with equal edge domination number and maximum matching cardinality are characterized. These two parameters are used to develop bounds on the vertex cover and total vertex cover numbers of graphs and a resulting chain of vertex covering, edge domination, and matching parameters is explored. In addition, the total vertex cover number is compared to the total domination number of ...

متن کامل

Small Edge Dominating Sets of Regular Graphs

An edge dominating set F of a graph G is a subset of E(G) such that every edge in E(G) \ F is incident with at least one vertex that is an end-point of an edge in F . Edge dominating sets of small cardinality are of interest. We refer to the size of a smallest edge dominating set of a graph G as the edge domination number of G and denote this by β(G). In this paper we improve all current known ...

متن کامل

On total dominating sets in graphs

A set S of vertices in a graph G(V,E) is called a dominating set if every vertex v ∈ V is either an element of S or is adjacent to an element of S. A set S of vertices in a graph G(V,E) is called a total dominating set if every vertex v ∈ V is adjacent to an element of S. The domination number of a graph G denoted by γ(G) is the minimum cardinality of a dominating set in G. Respectively the tot...

متن کامل

Trees with unique minimum total dominating sets

A set S of vertices of a graph G is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. We provide three equivalent conditions for a tree to have a unique minimum total dominating set and give a constructive characterization of such trees.

متن کامل

ذخیره 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: Theoretical Computer Science

سال: 2021

ISSN: ['1879-2294', '0304-3975']

DOI: https://doi.org/10.1016/j.tcs.2021.03.028