4 problems

For each integer $r\geq2$, define the Beraha number … A plane triangulation is a loopless plane graph whose faces all have size three. Beraha's conjecture. For every $r\geq2$ and e…

A plane triangulation is a loopless plane graph in which every face has size three. Let $P(G,t)$ be its chromatic polynomial, let $\tau=(1+\sqrt{5})/2$ be the golden ratio, and let…

A triangulation is a plane graph in which every face, including the outer face, is bounded by a triangle. The degree of a vertex is its number of incident edges. The bounded-except…

A triangulation is a plane graph in which every face, including the outer face, is bounded by a triangle. A dominating set of a graph is a set containing every vertex or a neighbor…