Perfect forests in graphs and their extensions
| Autor: | Gutin, Gregory, Yeo, Anders |
|---|---|
| Přispěvatelé: | Bonchi, Filippo, Puglisi, Simon J. |
| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
graphs Polynomial algorithms polynomial algorithms Mathematics of computing → Graph theory Discrete Mathematics (cs.DM) odd degree subgraphs perfect forests Computer Science - Data Structures and Algorithms FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Data Structures and Algorithms (cs.DS) Combinatorics (math.CO) Geometry and Topology Graphs Perfect forests Computer Science - Discrete Mathematics Odd degree subgraphs |
| Zdroj: | Gutin, G & Yeo, A 2021, Perfect Forests in Graphs and Their Extensions . in F Bonchi & S J Puglisi (eds), 46th International Symposium on Mathematical Foundations of Computer Science, MFCS 2021 ., 54, Schloss Dagstuhl-Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, Leibniz International Proceedings in Informatics, LIPIcs, vol. 202, 46th International Symposium on Mathematical Foundations of Computer Science, MFCS 2021, Tallinn, Estonia, 23/08/2021 . https://doi.org/10.4230/LIPIcs.MFCS.2021.54 |
| ISSN: | 1097-0118 0364-9024 |
| DOI: | 10.1002/jgt.22841 |
| Popis: | Let G be a graph on n vertices. For i ∈ {0,1} and a connected graph G, a spanning forest F of G is called an i-perfect forest if every tree in F is an induced subgraph of G and exactly i vertices of F have even degree (including zero). An i-perfect forest of G is proper if it has no vertices of degree zero. Scott (2001) showed that every connected graph with even number of vertices contains a (proper) 0-perfect forest. We prove that one can find a 0-perfect forest with minimum number of edges in polynomial time, but it is NP-hard to obtain a 0-perfect forest with maximum number of edges. We also prove that for a prescribed edge e of G, it is NP-hard to obtain a 0-perfect forest containing e, but we can find a 0-perfect forest not containing e in polynomial time. It is easy to see that every graph with odd number of vertices has a 1-perfect forest. It is not the case for proper 1-perfect forests. We give a characterization of when a connected graph has a proper 1-perfect forest. LIPIcs, Vol. 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021), pages 54:1-54:13 |
| Databáze: | OpenAIRE |
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