Detecting holes and antiholes in graphs
| dc.contributor.author | Nikolopoulos, S. D. | en |
| dc.contributor.author | Palios, L. | en |
| dc.date.accessioned | 2015-11-24T17:01:33Z | |
| dc.date.available | 2015-11-24T17:01:33Z | |
| dc.identifier.issn | 0178-4617 | - |
| dc.identifier.uri | https://olympias.lib.uoi.gr/jspui/handle/123456789/10944 | |
| dc.rights | Default Licence | - |
| dc.subject | holes | en |
| dc.subject | antiholes | en |
| dc.subject | weakly chordal graphs | en |
| dc.subject | co-connectivity | en |
| dc.subject | weakly triangulated graphs | en |
| dc.subject | linear-time algorithms | en |
| dc.subject | recognition | en |
| dc.title | Detecting holes and antiholes in graphs | en |
| heal.abstract | In this paper we study the problems of detecting holes and antiholes in general undirected graphs, and we present algorithms for these problems. For an input graph G on n vertices and m edges, our algorithms run in O(n + m(2)) time and require O(n m) space; we thus provide a solution to the open problem posed by Hayward et al. asking for an O(n(4))-time algorithm for finding holes in arbitrary graphs. The key element of the algorithms is the use of the depth-first-search traversal on appropriate auxiliary graphs in which moving between any two adjacent vertices is equivalent to walking along a P-4 (i.e., a chordless path on four vertices) of the input graph or on its complement, respectively. The approach can be generalized so that for a fixed constant k >= 5 we obtain an O(n(k-1))-time algorithm for the detection of a hole (antihole resp.) on at least k vertices. Additionally, we describe a different approach which allows us to detect antiholes in graphs that do not contain chordless cycles on five vertices in O(n + m(2)) time requiring O(n + m) space. Again, for a fixed constant k >= 6, the approach can be extended to yield O(n(k-2))-time and O(n(2))-space algorithms for detecting holes (antiholes resp.) on at least k vertices in graphs which do not contain holes (antiholes resp.) on k - 1 vertices. Our algorithms are simple and can be easily used in practice. Finally, we also show how our detection algorithms can be augmented so that they return a hole or an antihole whenever such a structure is detected in the input graph; the augmentation takes O(n + m) time and space. | en |
| heal.access | campus | - |
| heal.fullTextAvailability | TRUE | - |
| heal.identifier.primary | DOI 10.1007/s00453-006-1225-y | - |
| heal.journalName | Algorithmica | en |
| heal.journalType | peer reviewed | - |
| heal.language | en | - |
| heal.publicationDate | 2007 | - |
| heal.recordProvider | Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μηχανικών Ηλεκτρονικών Υπολογιστών και Πληροφορικής | el |
| heal.type | journalArticle | - |
| heal.type.el | Άρθρο Περιοδικού | el |
| heal.type.en | Journal article | en |
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