2016/02/01 by Marcin Kamiński, Kamiński, Marcin, Jean‐Florent Raymond +3
Computer Science · Mathematics · #06A07 #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #G.2.2 #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1602.00733
openalex publication_date 2016/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A well-quasi-order is an order which contains no infinite decreasing sequence and no infinite collection of incomparable elements. In this paper, we consider graph classes defined by excluding one graph as contraction. More precisely, we give a complete characterization of graphs H such that the class of H-contraction-free graphs is well-quasi-ordered by the contraction relation. This result is the contraction analogue on the previous dichotomy theorems of Damsaschke [Induced subgraphs and well-quasi-ordering, Journal of Graph Theory, 14(4):427-435, 1990] on the induced subgraph relation, Ding [Subgraphs and well-quasi-ordering, Journal of Graph Theory, 16(5):489-502, 1992] on the subgraph relation, and Błasiok et al. [Induced minors and well-quasi-ordering, ArXiv e-prints, 1510.07135, 2015] on the induced minor relation.