3 problems

Dynamical splitting conjecture. In the case $K=1$, the shifted state with $a<0$ leads to a solitary wave that moves towards the vertex point at $x=0$ along the only incoming edge,…

Let $G$ be the tensor product of two distinct star graphs $S_n$ and $S_m$. Star-graph tensor-product conjecture. The $b$-chromatic number of $G$ is $m+n+1$. This conjecture propose…

Let $S_n$ be the star graph on $n$ vertices, with central vertex labeled by $1$, and let … For a vertex subset $S$, write $Y_S$ for the associated cluster-algebra element and…