Some results on the k-strong parity property in a graph

2025/05/26 by Jie Wu, Wu, Jie · 3 citations
Computer Science · Mathematics · #Graph Labeling and Dimension Problems #Advanced Graph Theory Research #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2505.20352

Abstract

A graph G has the k-strong parity property if for any X⊆ V(G) with |X| even, G contains a spanning subgraph F with d_F(u)≡1 (mod 2) for each u∈ X and d_F(v)∈\k,k+2,k+4,…\ for each v∈ V(G)∖ X, where k≥2 is an even integer. Kano and Matsumura proposed a characterization for a graph with the k-strong parity property (M. Kano, H. Matsumura, Odd-even factors of graphs, Graphs Combin. 41 (2025) 55). In this paper, we first give a size condition for a graph to have the k-strong parity property. Then we establish a signless Laplacian spectral radius condition to guarantee that a graph has the k-strong parity property.

Cited by

• Distance spectral radius for a graph to be k-critical with respect to [1,b]-odd factor
• Sufficient conditions for even factors in graphs
• Generalized toughness and Q-index in a graph

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