منابع مشابه
Directed Tree-Width
* Partially supported by NSF under Grant No. DMS-9701598. † Research partially supported by NSF under Grant No. DMS-9401981 and by DIMACS Center, Rutgers University, New Brunswick, NJ 08903. ‡ Partially supported by ONR under Contract No. N00014-97-1-0512. §Partially supported by NSF under Grant No. DMS-9623031, by NSA under Contract No. MDA904-98-1-0517, and by DIMACS Center, Rutgers Universit...
متن کاملDirected tree-width examples
In [1] Johnson, Robertson, Seymour and Thomas define the notion of directed tree-width dtw(D) of a directed graph D. They ask whether dtw(D) ≥ k− 1 implies that D has a haven of order k. A negative answer is given. Furthermore they define a generalisation of the robber and cops game of [3] to digraphs. They ask whether it is true that if k cops can catch the robber on a digraph, then they can d...
متن کاملBounding connected tree-width
Diestel and Müller showed that the connected tree-width of a graph G, i. e., the minimum width of any tree-decomposition with connected parts, can be bounded in terms of the tree-width of G and the largest length of a geodesic cycle in G. We improve their bound to one that is of correct order of magnitude. Finally, we construct a graph whose connected tree-width exceeds the connected order of a...
متن کاملOn tree-partition-width
A tree-partition of a graph G is a proper partition of its vertex set into ‘bags’, such that identifying the vertices in each bag produces a forest. The tree-partition-width of G is the minimum number of vertices in a bag in a tree-partition of G. An anonymous referee of the paper by Ding and Oporowski [J. Graph Theory, 1995] proved that every graph with tree-width k ≥ 3 and maximum degree ∆ ≥ ...
متن کاملConnected tree-width
The connected tree-width of a graph is the minimum width of a treedecomposition whose parts induce connected subgraphs. Long cycles are examples of graphs that have small tree-width but large connected tree-width. We show that a graph has small connected tree-width if and only if it has small tree-width and contains no long geodesic cycle. We further prove a connected analogue of the duality th...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2001
ISSN: 0095-8956
DOI: 10.1006/jctb.2000.2031