5 problems

Let $G$ be a bridgeless cubic graph, and let $P_{10}$ denote the Petersen graph. An $H$-coloring of a cubic graph $G$ is a mapping $f:E(G)\rightarrow E(H)$ such that for every vert…

Let $n\re1$, set $m=n+5$, and let a graph be $p$-optimal if it maximizes all-terminal reliability $R(G,p)$ among $(n,m)$-graphs. A balanced weak subdivision of the Petersen graph i…

Let $C_m$ be the cycle graph on $m$ vertices, $K_2$ and $C_3$ the indicated factors, and let $G$ be the Petersen graph. For nonnegative exponents, the displayed Cartesian products…

Petersen graph flow-number conjecture.

Chromatic separation conjecture. (a) Two signed Petersen graphs that are not switching isomorphic have different zero-free chromatic polynomials; in particular, they have different…