8 problems

Carragher et al.'s conjecture. The subdivided complete graph $K_n^{1/m}$ is locatable if and only if

Unboundedness conjecture.

Let $P_n$ be an equilateral triangular grid graph with $n$ vertices on each side. Lions clear vertices they visit while contamination spreads along unblocked edges. Triangular-grid…

Consider a strip discretized by a triangular grid graph, with height $n$, and suppose all lions must move simultaneously at every time step. Simultaneous-motion insufficiency conje…

Let the square grid graph have $n\times n$ vertices, with contamination initially occupying every vertex except those occupied by lions. Lions move along edges, clearing vertices t…

Pyramid path-search conjecture. If $s_l=1+2+\ldots+l$ for some $l$, then

Let $F_k$ be the channel graph of depth $k$, with vacancy probability $q$, and consider algorithms that perform local path search in $F_k$. Unilateral depth-first-search optimality…

Let $F_k$ be the channel graph of depth $k$, let $q$ be the vacancy probability, and let $E_1(F_k,q)$ denote the expected number of probes made by unilateral depth-first search. Un…