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Article Dans Une Revue Discrete Mathematics Année : 2016

The 3/5-conjecture for weakly $S(K_{1,3})$-free forests

Simon Schmidt
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Résumé

The 3/5-conjecture for the domination game states that the game domination numbers of an isolate-free graph G on n vertices are bounded as follows: γ g (G) ≤ 3n 5 and γ ′ g (G) ≤ 3n+2 5. Recent progress have been done on the subject and the conjecture is now proved for graphs with minimum degree at least 2. One powerful tool, introduced by Bujtás is the so-called greedy strategy for Dominator. In particular, using this strategy, she has proved the conjecture for isolate-free forests without leafs at distance 4. In this paper, we improve this strategy to extend the result to the larger class of weakly S(K 1,3)-free forests, where a weakly $S(K_{1,3})$-free forest F is an isolate-free forest without induced $S(K_{ 1,3})$, whose leafs are leafs of F as well.
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Dates et versions

hal-01215891 , version 1 (16-10-2015)

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Simon Schmidt. The 3/5-conjecture for weakly $S(K_{1,3})$-free forests. Discrete Mathematics, 2016, 339 (11), pp.2767-2774. ⟨hal-01215891⟩
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