2024/12/26 by Shohei Koizumi, Yusuke Suzuki, Koizumi, Shohei +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2412.19074
openalex publication_date 2024/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we discuss matching extendability of optimal 1-projective plane graphs (abbreviated as O1PPG), which are drawn on the projective plane P2 so that every edge crosses another edge at most once, and has n vertices and exactly 4n- 4 edges. We first show that every O1PPG of even order is 1-extendable. Next, we characterize 2-extendable O1PPG's in terms of a separating cycle consisting of only non-crossing edges. Moreover, we characterize O1PPG's having connectivity exactly 5. Using the characterization, we further identify three independent edges in those graphs that are not extendable.