Computing the forcing spectrum of outerplanar graphs in polynomial time
The forcing number of a graph with a perfect matching M is the minimum number of edges in M whose endpoints need to be deleted, such that the remaining graph only has a single perfect matching. This number is of great interest in theoretical chemistry, since it conveys information about the structur...
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| Published in: | Discrete Applied Mathematics Vol. 377; pp. 204 - 217 |
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31.12.2025
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| Abstract | The forcing number of a graph with a perfect matching M is the minimum number of edges in M whose endpoints need to be deleted, such that the remaining graph only has a single perfect matching. This number is of great interest in theoretical chemistry, since it conveys information about the structural properties of several interesting molecules. On the other hand, in bipartite graphs the forcing number corresponds to the famous feedback vertex set problem in digraphs.
Determining the complexity of finding the smallest forcing number of a given planar graph is still a widely open and important question in this area, originally proposed by Afshani, Hatami, and Mahmoodian in 2004. We take a first step towards the resolution of this question by providing an algorithm that determines the set of all possible forcing numbers of an outerplanar graph in polynomial time. This is the first polynomial-time algorithm concerning this problem for a class of graphs of comparable or greater generality. |
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| AbstractList | The forcing number of a graph with a perfect matching M is the minimum number of edges in M whose endpoints need to be deleted, such that the remaining graph only has a single perfect matching. This number is of great interest in theoretical chemistry, since it conveys information about the structural properties of several interesting molecules. On the other hand, in bipartite graphs the forcing number corresponds to the famous feedback vertex set problem in digraphs.
Determining the complexity of finding the smallest forcing number of a given planar graph is still a widely open and important question in this area, originally proposed by Afshani, Hatami, and Mahmoodian in 2004. We take a first step towards the resolution of this question by providing an algorithm that determines the set of all possible forcing numbers of an outerplanar graph in polynomial time. This is the first polynomial-time algorithm concerning this problem for a class of graphs of comparable or greater generality. |
| Author | Kreßin, Fabian Gorsky, Maximilian |
| Author_xml | – sequence: 1 givenname: Maximilian orcidid: 0009-0001-7816-7084 surname: Gorsky fullname: Gorsky, Maximilian email: m.gorsky@pm.me organization: Discrete Mathematics Group, Institute for Basic Science (IBS), Daejeon, South Korea – sequence: 2 givenname: Fabian surname: Kreßin fullname: Kreßin, Fabian email: fabian.kressin@tu-berlin.de organization: Technische Universität Berlin, Germany |
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| Cites_doi | 10.1016/j.dam.2015.08.024 10.1016/j.disc.2022.113249 10.1016/S0012-365X(97)00266-5 10.1021/ci00018a011 10.1007/BF01192587 10.1007/s10255-021-1010-3 10.1112/jlms/s2-17.3.369 10.1016/j.disc.2020.112124 10.1145/1103963.1103969 10.1137/0208032 10.1007/s10910-018-0944-z 10.1007/s10878-015-9986-3 10.1007/s10910-006-9208-4 10.1007/s40314-023-02228-7 10.1016/0012-365X(80)90037-0 10.1016/0095-8956(87)90021-9 10.1006/jagm.1995.1022 10.1016/0166-218X(95)00116-9 10.1016/j.cplett.2004.11.098 10.1090/S0002-9947-1932-1501641-2 10.1007/s10910-006-9133-6 10.1016/j.disc.2002.10.002 10.1002/jcc.540080432 10.46793/match.87-3.561L |
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| Keywords | Outerplanar graphs Forcing number Polynomial time algorithm Forcing spectrum Perfect matching Tight cut decomposition |
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| SubjectTerms | Forcing number Forcing spectrum Outerplanar graphs Perfect matching Polynomial time algorithm Tight cut decomposition |
| Title | Computing the forcing spectrum of outerplanar graphs in polynomial time |
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