2015/12/16 by Hongliang Lu, David G. L. Wang, Lu, Hongliang +1
Computer Science · Mathematics · #05C75 05C70 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #math.CO #msc:05C70 #msc:05C75
paper · pdf · doi:10.48550/arxiv.1512.05182
12 pages
arxiv created 2015/12/16 · openalex publication_date 2015/12/16 · arxiv updated 2015/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a connected general graph. Let f\colon V(G)→ \Z+ be a function. We show that G satisfies the Tutte-type condition o(G-S)≤ f(S)\qquadfor all vertex subsets S, if and only if it contains a colored Jf^*-factor for any 2-end-coloring, where Jf^*(v) is the union of all odd integers smaller than f(v) and the integer f(v) itself. This is a generalization of the (1,f)-odd factor characterization theorem, and answers a problem of Cui and Kano. We also derive an analogous characterization for graphs of odd orders, which addresses a problem of Akiyama and Kano.