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Please use this identifier to cite or link to this item: https://www.um.edu.mt/library/oar/handle/123456789/112528
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dc.contributor.authorCaro, Yair-
dc.contributor.authorLauri, Josef-
dc.contributor.authorZarb, Christina-
dc.date.accessioned2023-08-23T06:29:15Z-
dc.date.available2023-08-23T06:29:15Z-
dc.date.issued2017-
dc.identifier.citationCaro, Y., Lauri, J., & Zarb, C. (2017). Two short proofs of the perfect forest theorem. Theory & Applications Of Graphs, 4(1), 4.en_GB
dc.identifier.urihttps://www.um.edu.mt/library/oar/handle/123456789/112528-
dc.description.abstractA perfect forest is a spanning forest of a connected graph G, all of whose components are induced subgraphs of G and such that all vertices have odd degree in the forest. A perfect forest can be thought of as a generalization of a perfect matching since, in a matching, all components are trees on one edge. Scott first proved the Perfect Forest Theorem, namely, that every connected graph of even order has a perfect forest. Gutin then gave another proof using linear algebra. We give two very short proofs of the Perfect Forest Theorem which use only elementary notions from graph theory. Both of our proofs yield polynomial time algorithms for finding a perfect forest in a connected graph of even order.en_GB
dc.language.isoenen_GB
dc.publisherGeorgia Southern Universityen_GB
dc.rightsinfo:eu-repo/semantics/restrictedAccessen_GB
dc.subjectPerfect graphsen_GB
dc.subjectGraph theoryen_GB
dc.subjectGraphic methodsen_GB
dc.subjectMathematics -- Charts, diagrams, etc.en_GB
dc.titleTwo short proofs of the Perfect Forest Theoremen_GB
dc.typearticleen_GB
dc.rights.holderThe copyright of this work belongs to the author(s)/publisher. The rights of this work are as defined by the appropriate Copyright Legislation or as modified by any successive legislation. Users may access this work and can make use of the information contained in accordance with the Copyright Legislation provided that the author must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the prior permission of the copyright holder.en_GB
dc.description.reviewedpeer-revieweden_GB
dc.identifier.doi10.20429/tag.2017.040104-
dc.publication.titleTheory & Applications Of Graphsen_GB
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