2024/09/20 by Shang, Wangyi, Hajo Broersma, Broersma, Hajo +4
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2409.13491
openalex publication_date 2024/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We say that a graph G on n vertices is \H,F\-o-heavy if every induced subgraph of G isomorphic to H or F contains two nonadjacent vertices with degree sum at least n. Generalizing earlier sufficient forbidden subgraph conditions for hamiltonicity, in 2012, Li, Ryjáček, Wang and Zhang determined all connected graphs R and S of order at least 3 other than P3 such that every 2-connected \R,S\-o-heavy graph is hamiltonian. In particular, they showed that, up to symmetry, R must be a claw and S∈\P4,P5,C3,Z1,Z2,B,N,W\. In 2008, Čada extended Ryjáček's closure concept for claw-free graphs by introducing what we call the c-closure for claw-o-heavy graphs. We apply it here to characterize the structure of the c-closure of 2-connected \R,S\-o-heavy graphs, where R and S are as above. Our main results extend or generalize several earlier results on hamiltonicity involving forbidden or o-heavy subgraphs.