Kinnersley–West–Zamani 3/5-conjecture for isolate-free forests

About 12 years old · traced to

Let GG be an isolate-free forest of order nn. In the domination game, Dominator starts in Dominator−startgameDominator-start game, whose game domination number is denoted by γg(G)\gamma_g(G), while γg′(G)\gamma_g'(G) denotes the corresponding Staller-start game number.

Kinnersley–West–Zamani 3/5-conjecture.

γg(G)≤3n5andγg′(G)≤3n+25.\gamma_g(G) \leq \frac{3n}{5}\quad\text{and}\quad \gamma_g'(G) \leq \frac{3n+2}{5}.

This conjecture proposes the sharp upper bounds for the two domination-game variants on isolate-free forests; the paper presents it as an open problem.

References

Primary source

Csilla Bujtás, “Domination game on forests”, arXiv:1404.1382 (2014).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.