Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10311991" target="_blank" >RIV/00216208:11320/15:10311991 - isvavai.cz</a>
Alternative codes found
RIV/49777513:23520/15:43925867
Result on the web
<a href="http://dx.doi.org/10.1002/jgt.21832" target="_blank" >http://dx.doi.org/10.1002/jgt.21832</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.21832" target="_blank" >10.1002/jgt.21832</a>

Result language
angličtina
Original language name
Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs
Original language description
We prove that for all k-1 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 verticesand m edges, which improves the previously best-known O(n3) 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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