منابع مشابه
Tree-width and planar minors
Robertson and the second author [7] proved in 1986 that for all h there exists f(h) such that for every h-vertex simple planar graph H, every graph with no H-minor has tree-width at most f(h); but how small can we make f(h)? The original bound was an iterated exponential tower, but in 1994 with Thomas [9] it was improved to 2O(h 5); and in 1999 Diestel, Gorbunov, Jensen, and Thomassen [3] prove...
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We call H a minor of a graph G if H is obtainable from a subgraph of G by edge contractions. If g ≥ 2, the g-grid is the simple graph with vertices vij (1 ≤ i, j ≤ g) where vij and vi′j′ are adjacent if |i− i′|+ |j − j′| = 1; see Robertson and Seymour (1991). A tree-decomposition of a graph G , is a pair (T, S), where T is a tree and S = {St : t ∈ V (T )} is a family of subsets of V (G), called...
متن کاملSurfaces, Tree-Width, Clique-Minors, and Partitions
In 1971, Chartrand, Geller, and Hedetniemi conjectured that the edge set of a planar graph may be partitioned into two subsets, each of which induces an outerplanar graph. Some partial results towards this conjecture are presented. One of which, that a planar graph may be thus edge partitioned into two series-parallel graphs, has nice generalizations for graphs embedded onto an arbitrary surfac...
متن کاملLocal Tree-Width, Excluded Minors, and Approximation Algorithms
The local tree-width of a graph G = (V;E) is the function ltwG : N ! N that associates with every r 2 N the maximal tree-width of an r-neighborhood in G. Our main graph theoretic result is a decomposition theorem for graphs with excluded minors, which says that such graphs can be decomposed into trees of graphs of almost bounded local tree-width. As an application of this theorem, we show that ...
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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2015
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2014.09.003