On Maximal Chain Subgraphs and Covers of Bipartite Graphs

This suggests that we could enumerate all stories by enumerating all the minimal FAS s and by checking for each of them whether the resulting graph is a story (which can be done

At the end we shall additionally prove that in general every graph without isolated edges can be decomposed into (at most) 24 subgraphs consistent with the 1–2–3 Conjecture, while

We first prove that this problem can be solved in polynomial time for k ≤ 3 in any graph and that it is NP-complete for any fixed k ≥ 5 in the class of planar bipartite graphs of

In this subsection, we prove that computing the proper orientation number of a graph is still NP -hard for planar bipartite graphs of bounded degree.. The idea of our reduction