Abstract
| Original language | Undefined |
|---|---|
| Pages (from-to) | 282-299 |
| Number of pages | 18 |
| Journal | Journal of graph theory |
| Volume | 79 |
| Issue number | 4 |
| DOIs | |
| State | Published - Aug 2015 |
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Keywords
- MSC-05C
- METIS-314967
- IR-98274
- EWI-26316
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Linear-time algorithms for scattering number and hamilton-connectivity of interval graphs. / Broersma, Haitze J.; Fiala, Jiri; Golovach, Petr A.; Kaiser, Tomas; Paulusma, Daniël; Proskurowski, Andrzej.
In: Journal of graph theory, Vol. 79, No. 4, 08.2015, p. 282-299.Research output: Scientific - peer-review › Article
TY - JOUR
T1 - Linear-time algorithms for scattering number and hamilton-connectivity of interval graphs
AU - Broersma,Haitze J.
AU - Fiala,Jiri
AU - Golovach,Petr A.
AU - Kaiser,Tomas
AU - Paulusma,Daniël
AU - Proskurowski,Andrzej
N1 - eemcs-eprint-26316
PY - 2015/8
Y1 - 2015/8
N2 - We prove that for all integers k<0 an interval graph is -(k+1)-Hamilton-connected if and only if its scattering number is at most k. This complements a previously known fact that an interval graph has a nonnegative scattering number if and only if it contains a Hamilton cycle, as well as a characterization of interval graphs with positive scattering numbers in terms of the minimum size of a path cover. We also give an O(n+m) time algorithm for computing the scattering number of an interval graph with n vertices and m edges, which improves the previously best-known O(n^3) time bound for solving this problem. As a consequence of our two results, the maximum k for which an interval graph is k-Hamilton-connected can be computed in O(n+m) time.
AB - We prove that for all integers k<0 an interval graph is -(k+1)-Hamilton-connected if and only if its scattering number is at most k. This complements a previously known fact that an interval graph has a nonnegative scattering number if and only if it contains a Hamilton cycle, as well as a characterization of interval graphs with positive scattering numbers in terms of the minimum size of a path cover. We also give an O(n+m) time algorithm for computing the scattering number of an interval graph with n vertices and m edges, which improves the previously best-known O(n^3) time bound for solving this problem. As a consequence of our two results, the maximum k for which an interval graph is k-Hamilton-connected can be computed in O(n+m) time.
KW - MSC-05C
KW - METIS-314967
KW - IR-98274
KW - EWI-26316
U2 - 10.1002/jgt.21832
DO - 10.1002/jgt.21832
M3 - Article
VL - 79
SP - 282
EP - 299
JO - Journal of graph theory
T2 - Journal of graph theory
JF - Journal of graph theory
SN - 0364-9024
IS - 4
ER -