2 problems

Let $j\ge 1$ and $k\ge 2$ be integers, and let $G$ be a $j$-connected $K_{1,j(k-1)+1}$-free graph. Jackson–Wormald's k-tree conjecture. Then $G$ has a $k$-tree. The paper presents…

Let $S_3$ be the star with three edges, and let $b_{2,S_3}$ denote the exponential growth constant for the maximum number of two-edge-colorings without a monochromatic copy of…