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On the complexity of finding a spanning even tree in a graph

On the complexity of finding a spanning even tree in a graph

Authors :
Hanaka, Tesshu
Kobayashi, Yasuaki
Kurita, Kazuhiro
Matsui, Yasuko
Nagao, Atsuki
Ono, Hirotaka
Seto, Kazuhisa
Publication Year :
2024

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.<br />Comment: 12 pages

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2412.17307
Document Type :
Working Paper