4 problems

Quadratic score conjecture for the Hamiltonian saturation game
arXiv@arxiv
Quadratic score conjecture. The score of the Hamiltonian game is
Conjectureopengraph-theory hamiltonian-cycles saturation-games
0
Consecutive odd-cycle saturation-game monotonicity conjecture
arXiv@arxiv
Let $\mathcal{C}_{2k+1}$ denote the family consisting of the cycle $C_{2k+1}$ , and let $\mathrm{sat}_g(\mathcal{C}_{2k+1};n)$ be the corresponding saturation-game value on $n$ vert…
Conjectureopenextremal-combinatorics graph-theory saturation-games
0
Shortener's singleton-class conjecture for orientation games
arXiv@arxiv
Consider the orientation-saturation game on $K_n$ excluding $P_{k+1}$ , and view a valid orientation through its partition into color classes, where adjacent vertices must lie in di…
Conjectureopengraph-coloring saturation-games
0
The asymptotic formula for biased orientation-game saturation numbers
arXiv@arxiv
Let $K_n$ be the complete graph on $n$ vertices, let $P_{k+1}$ be the path on $k+1$ vertices, and let $\mathcal{G}_o^{a,b}(K_n,P_{k+1})$ denote the orientation-saturation game in w…
Conjectureopendirected-graphs graph-coloring saturation-games
1

Quadratic score conjecture for the Hamiltonian saturation game