2018/06/25 by Hongliang Lu, David G. L. Wang, Lu, Hongliang +1
Computer Science · Engineering · Mathematics · #05C75 05C70 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #graph theory and CDMA systems #math.CO #msc:05C70 #msc:05C75
paper · pdf · doi:10.48550/arxiv.1806.09357
5 pages
arxiv created 2018/06/25 · openalex publication_date 2018/06/25 · arxiv updated 2018/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a connected general graph of even order, with a function f\colon V(G)→\Z+. We obtain that G satisfies the Tutte's condition o(G-S)≤ ∑v∈ Sf(v)\qquadfor any nonempty set S⊂ V(G), with respect to f if and only if G contains an H-factor for any function H\colon V(G)→ 2^\N such that H(v)∈ \Jf(v), Jf+(v)\ for each v∈ V(G), where the set Jf(v) consists of the integer f(v) and all positive odd integers less than f(v), and the set J+f(v) consists of positive odd integers less than or equal to f(v)+1. We also obtain a characterization for graphs of odd order satisfying the Tutte's condition with respect to a function.