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THE DOMINATION GAME ON SPLIT GRAPHS
Part of
- Graph theory
- Game theory
TIJO JAMES, SANDI KLAVŽAR, AMBAT VIJAYAKUMAR
Journal:

Bulletin of the Australian Mathematical Society / Volume 99 / Issue 2 / April 2019

Published online by Cambridge University Press:

12 November 2018, pp. 327-337

Print publication:

April 2019
- Article
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We investigate the domination game and the game domination number $\unicode[STIX]{x1D6FE}_{g}$ in the class of split graphs. We prove that $\unicode[STIX]{x1D6FE}_{g}(G)\leq n/2$ for any isolate-free $n$-vertex split graph $G$, thus strengthening the conjectured $3n/5$ general bound and supporting Rall’s $\lceil n/2\rceil$-conjecture. We also characterise split graphs of even order with $\unicode[STIX]{x1D6FE}_{g}(G)=n/2$.