منابع مشابه
Induced minors and well-quasi-ordering
A graph H is an induced minor of a graph G if it can be obtained from an induced subgraph of G by contracting edges. Otherwise, G is said to be H-induced minor-free. Robin Thomas showed that K4-induced minor-free graphs are well-quasi-ordered by induced minors [Graphs without K4 and well-quasi-ordering, Journal of Combinatorial Theory, Series B, 38(3):240 – 247, 1985]. We provide a dichotomy th...
متن کاملGraph minors. IV. Tree-width and well-quasi-ordering
K. Wagner conjectured that if G1, GZ, .,. is any countable sequence of finite graphs, then there exist i, j with j> i> 1 such that Gi is isomorphic to a minor of G,. Kruskal proved this when G1, G2, . . . are all trees. We prove a strengthening of Kruskal’s result-Wagner’s conjecture is true for all sequences in which G1 is planar. We hope to show in a future paper that Wagner’s conjecture is t...
متن کاملSubgraphs and well-quasi-ordering
Let % be a class of graphs and let i be the subgraph or the induced subgraph relation. We call % an idea/ (with respect to I) if G I G' E % implies that G E %. In this paper, we study the ideals that are well-quasiordered by I. The following are our main results. If 5 is the subgraph relation, we characterize the well-quasi-ordered ideals in terms of excluding subgraphs. If I is the induced sub...
متن کاملWell-Quasi-Ordering, Overview and its Applications
This talk shows theorems, techniques, and applications of well-quasi-ordering (WQO). First, we introduce what is WQO, and Kruskaltype theorems on various data structures [31, 15, 16, 23, 34, 33]. The basic proof technique, minimal bad sequence (MBS), will be introduced for the simplest case, Higman’s Lemma. Then, WQO will be extended to better-quasi-ordering (BQO) for infinite data structures [...
متن کاملRank-Width and Well-Quasi-Ordering
Robertson and Seymour (1990) proved that graphs of bounded tree-width are well-quasi-ordered by the graph minor relation. By extending their arguments, Geelen, Gerards, and Whittle (2002) proved that binary matroids of bounded branch-width are well-quasi-ordered by the matroid minor relation. We prove another theorem of this kind in terms of rank-width and vertex-minors. For a graph G = (V,E) a...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2019
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2018.05.005