Conjecture Let be a graph and let such that for any pair there are edge-disjoint paths from to in . Then contains edge-disjoint trees, each of which contains .
Conjecture There is an integer-valued function such that if is any -connected graph and and are any two vertices of , then there exists an induced path with ends and such that is -connected.
Let be a simple graph, and for every list assignment let be the maximum number of vertices of which are colorable with respect to . Define , where the minimum is taken over all list assignments with for all .
Conjecture [2] Let be a graph with list chromatic number and . Then
Conjecture Let be an integer. For every integer , there exists an integer such that for every digraph , either has a pairwise-disjoint directed cycles of length at least , or there exists a set of at most vertices such that has no directed cycles of length at least .
Conjecture For every , the sequence in consisting of copes of and copies of has the fewest number of distinct subsequence sums over all zero-free sequences from of length .
Problem What is the largest connected planar graph of minimum degree 3 which has everywhere positive combinatorial curvature, but is not a prism or antiprism?