Abstract:Recent results established the maximum forest number $f(B)$ for balanced bipartite graphs under Ore-type degree sum conditions. In this paper, we extend these results by determining the exact value of the maximum forest number as a closed-form formula for general bipartite graphs under Ore-type conditions, answering an open question posed by Yu. We prove that the maximum forest number is bounded by a discrete optimization over at most six critical structural coordinate points dictated by hyperbolic density constraints. Furthermore, we establish that deciding whether a specific balanced bipartite graph on $2n$ vertices has a forest number of at least $n+2$ is NP-complete. This implies that while the maximum possible forest number can be exactly bounded, computing the exact forest number for a given graph remains computationally intractable, and a simple structural characterization via finite forbidden induced subgraphs cannot exist unless P = NP.
From: Daniel Ilkovic [view email]
[v1]
Thu, 25 Jun 2026 08:47:12 UTC (10 KB)
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