Degree condition for maximum-length cycles in bipartite digraphs
Degree condition for maximum-length cycles in bipartite digraphs
Let be a bipartite digraph with colour classes and such that . For vertices and in opposite colour classes with , consider the degree condition
Maximum-cycle degree conjecture. If this inequality holds whenever and lie in opposite colour classes and , then contains an oriented cycle of length .
This is an Ore-type sufficient condition for a bipartite digraph to contain a cycle meeting every vertex of its smaller colour class. The source states that the conjecture is proved in the balanced case , while the general case remains open.
Sources & referencesView supporting material
Primary source
Janusz Adamus and Lech Adamus, “A degree condition for cycles of maximum length in bipartite digraphs”, arXiv:1101.4973 (2012).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.