Total Version of the Domination Game

نویسندگان

  • Michael A. Henning
  • Sandi Klavzar
  • Douglas F. Rall
چکیده

In this paper, we continue the study of the domination game in graphs introduced by Brešar, Klavžar, and Rall [SIAM J. Discrete Math. 24 (2010) 979–991]. We study the total version of the domination game and show that these two versions differ significantly. We present a key lemma, known as the Total Continuation Principle, to compare the Dominator-start total domination game and the Staller-start total domination game. Relationships between the game total domination number and the total domination number, as well as between the game total domination number and the domination number, are established.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Paired-Domination Game Played in Graphs

In this paper, we continue the study of the domination game in graphs introduced by Bre{v{s}}ar, Klav{v{z}}ar, and Rall. We study the paired-domination version of the domination game which adds a matching dimension to the game. This game is played on a graph $G$ by two players, named Dominator and Pairer. They alternately take turns choosing vertices of $G$ such that each vertex chosen by Domin...

متن کامل

On the Computational Complexity of the Domination Game

The domination game is played on an arbitrary graph $G$ by two players, Dominator and Staller. It is known that verifying whether the game domination number of a graph is bounded by a given integer $k$ is PSPACE-complete. On the other hand, it is showed in this paper that the problem can be solved for a graph $G$ in $mathcal O(Delta(G)cdot |V(G)|^k)$ time. In the special case when $k=3$ and the...

متن کامل

Trees with equal total domination and game total domination numbers

In this paper, we continue the study of the total domination game in graphs introduced in [Graphs Combin. 31(5) (2015), 1453–1462], where the players Dominator and Staller alternately select vertices of G. Each vertex chosen must strictly increase the number of vertices totally dominated, where a vertex totally dominates another vertex if they are neighbors. This process eventually produces a t...

متن کامل

Transversal Game on Hypergraphs and the 3/4-Conjecture on the Total Domination Game

The 34 -Game Total Domination Conjecture posed by Henning, Klavžar and Rall [Combinatorica, to appear] states that if G is a graph on n vertices in which every component contains at least three vertices, then γtg(G) ≤ 34n, where γtg(G) denotes the game total domination number of G. Motivated by this conjecture, we raise the problem to a higher level by introducing a transversal game in hypergra...

متن کامل

The 4/5 upper bound on the game total domination number

The recently introduced total domination game is studied. This game is played on a graph G by two players, named Dominator and Staller. They alternately take turns choosing vertices of G such that each chosen vertex totally dominates at least one vertex not totally dominated by the vertices previously chosen. Dominator’s goal is to totally dominate the graph as fast as possible, and Staller wis...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Graphs and Combinatorics

دوره 31  شماره 

صفحات  -

تاریخ انتشار 2015