2024/12/23 by Tesshu Hanaka, Hanaka, Tesshu, Yasuaki Kobayashi +11
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2412.17307
openalex publication_date 2024/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.