Year: 2024
Type: preprint
Abstract: A tree is said to be even if for every pair of distinct leaves, the length of the unique path between them is even. In this paper we discuss the problem of determining whether an input graph has a spanning even tree. Hofmann and Walsh [Australas. J Comb. 35, 2006] proved that this problem can be solved in polynomial time on bipartite graphs. In contrast to this, we show that this problem is NP-complete even on planar graphs. We also give polynomial-time algorithms for several restricted classes of graphs, such as split graphs, cographs, cobipartite graphs, unit interval graphs, and block graphs.
Source: arXiv (Cornell University)
Authors: Hanaka, Tesshu, Kobayashi, Yasuaki, Kurita, Kazuhiro, Matsui, Yasuko, Nagao, Atsuki, Ono, Hirotaka, Seto, Kazuhisa
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405767848