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Abstract
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A set S of vertices of a graph G = (V,E) without isolated vertex is a total dominating
set if every vertex of V (G) is adjacent to some vertex in S. The total domination number
γt(G) is the minimum cardinality of a total dominating set of G. The game total
domination subdivision number of a graph G is defined by the following game. Two
players D and A, D playing first, alternately mark or subdivide an edge of G which is
not yet marked nor subdivided. The game ends when all the edges of G are marked or
subdivided and results in a new graph G. The purpose of D is to minimize the total
domination number γt(G) of G while A tries to maximize it. If both A and D play
according to their optimal strategies, γt(G) is well defined. We call this number the
game total domination subdivision number of G and denote it by γgt(G). In this paper
we initiate the study of the game total domination subdivision number of a graph and
present some (sharp) bounds for this parameter.
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