| GANIAN, Robert, Petr HLINĚNÝ, Jan OBDRŽÁLEK, Joachim KNEIS, Daniel MEISTER, Somnath SIKDAR a Peter ROSSMANITH. Are there any good digraph width measures? Journal of Combinatorial Theory, Ser B. Academic Press, 2016, roč. 116, č. 1, s. 250-286. ISSN 0095-8956. Dostupné z: https://dx.doi.org/10.1016/j.jctb.2015.09.001. |
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@article{1323142,
author = {Ganian, Robert and Hliněný, Petr and Obdržálek, Jan and Kneis, Joachim and Meister, Daniel and Sikdar, Somnath and Rossmanith, Peter},
article_number = {1},
doi = {http://dx.doi.org/10.1016/j.jctb.2015.09.001},
keywords = {Tree-width; Digraph width; Directed minor; Cops-and-robber game},
language = {eng},
issn = {0095-8956},
journal = {Journal of Combinatorial Theory, Ser B},
title = {Are there any good digraph width measures?},
volume = {116},
year = {2016}
}
TY - JOUR
ID - 1323142
AU - Ganian, Robert - Hliněný, Petr - Obdržálek, Jan - Kneis, Joachim - Meister, Daniel - Sikdar, Somnath - Rossmanith, Peter
PY - 2016
TI - Are there any good digraph width measures?
JF - Journal of Combinatorial Theory, Ser B
VL - 116
IS - 1
SP - 250-286
EP - 250-286
PB - Academic Press
SN - 00958956
KW - Tree-width
KW - Digraph width
KW - Directed minor
KW - Cops-and-robber game
N2 - Many width measures for directed graphs have been proposed in the last few years in pursuit of generalizing (the notion of) treewidth to directed graphs. However, none of these measures possesses, at the same time, the major properties of treewidth, namely, 1. being algorithmically useful , that is, admitting polynomial-time algorithms for a large class of problems on digraphs of bounded width (e.g. the problems definable in MSO1MSO1); 2. having nice structural properties such as being (at least nearly) monotone under taking subdigraphs and some form of arc contractions (property closely related to characterizability by particular cops-and-robber games). We investigate the question whether the search for directed treewidth counterparts has been unsuccessful by accident, or whether it has been doomed to fail from the beginning. Our main result states that any reasonable width measure for directed graphs which satisfies the two properties above must necessarily be similar to treewidth of the underlying undirected graph.
ER -
GANIAN, Robert, Petr HLINĚNÝ, Jan OBDRŽÁLEK, Joachim KNEIS, Daniel MEISTER, Somnath SIKDAR a Peter ROSSMANITH. Are there any good digraph width measures? \textit{Journal of Combinatorial Theory, Ser B}. Academic Press, 2016, roč.~116, č.~1, s.~250-286. ISSN~0095-8956. Dostupné z: https://dx.doi.org/10.1016/j.jctb.2015.09.001.
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