Unsolved Problems

The deck of a graph $G$ is the multiset consisting of all unlabelled subgraphs obtained from $G$ by deleting a vertex in all possible ways (counted ac...

Conjecture For every graph with no bridge, there is a list of cycles so that every edge is contained in exactly two....

Conjecture If $G$ is a bridgeless cubic graph, then there exist 6 perfect matchings $M_1,\ldots,M_6$ of $G$ with the property that every edge of $G$ i...

Conjecture Every bridgeless graph has a nowhere-zero 5-flow....

Conjecture Every simple digraph of order $n$ with minimum outdegree at least $r$ has a cycle with length at most $\lceil n/r\rceil$...