3 problems

Let $G$ and $H$ be graphs. A pair $(G,H)$ is Ramsey-infinite if it has infinitely many Ramsey-minimal graphs. An odd star is a star with an odd number of leaves, and a $K_2$-compon…

Let $S_a$ be the start-central star with parameter $a$, and let $P_b^\mathrm{alt}$ be an alternating path of order $b$. Star–alternating-path conjecture. For any $a \ge 3$ and…

Let $S_a$ be the start-central star with parameter $a$, and let $P_b^\mathrm{mon}$ be a monotone path of order $b$. Star–monotone-path conjecture. For any $a \ge 3$ and $b \ge 4$,…