On the path partition of graphs
Let \(G\) be a graph of order \(n\). The maximum and minimum degree of \(G\) are denoted by \(\Delta\) and \(\delta\), respectively. The path partition number \(\mu(G)\) of a graph \(G\) is the minimum number of paths needed to partition the vertices of \(G\). Magnant, Wang and Yuan conjectured that...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2023-07-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | https://www.opuscula.agh.edu.pl/vol43/6/art/opuscula_math_4340.pdf |
| _version_ | 1827895746478735360 |
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| author | Mekkia Kouider Mohamed Zamime |
| author_facet | Mekkia Kouider Mohamed Zamime |
| author_sort | Mekkia Kouider |
| collection | DOAJ |
| description | Let \(G\) be a graph of order \(n\). The maximum and minimum degree of \(G\) are denoted by \(\Delta\) and \(\delta\), respectively. The path partition number \(\mu(G)\) of a graph \(G\) is the minimum number of paths needed to partition the vertices of \(G\). Magnant, Wang and Yuan conjectured that \[\mu(G)\leq\max \left\{\frac{n}{\delta+1},\frac{(\Delta-\delta)n}{\Delta+\delta}\right\}.\] In this work, we give a positive answer to this conjecture, for \(\Delta\geq 2\delta\). |
| first_indexed | 2024-03-12T22:25:08Z |
| format | Article |
| id | doaj.art-eab3697f01754c908846ac84e4a626ea |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-03-12T22:25:08Z |
| publishDate | 2023-07-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-eab3697f01754c908846ac84e4a626ea2023-07-22T07:15:49ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742023-07-01436829839https://doi.org/10.7494/OpMath.2023.43.6.8294340On the path partition of graphsMekkia Kouider0Mohamed Zamime1University Paris Sud, FranceUniversity Yahia Fares of Medea, Department of Technology, Mathematics Laboratory and its Applications, Medea, AlgeriaLet \(G\) be a graph of order \(n\). The maximum and minimum degree of \(G\) are denoted by \(\Delta\) and \(\delta\), respectively. The path partition number \(\mu(G)\) of a graph \(G\) is the minimum number of paths needed to partition the vertices of \(G\). Magnant, Wang and Yuan conjectured that \[\mu(G)\leq\max \left\{\frac{n}{\delta+1},\frac{(\Delta-\delta)n}{\Delta+\delta}\right\}.\] In this work, we give a positive answer to this conjecture, for \(\Delta\geq 2\delta\).https://www.opuscula.agh.edu.pl/vol43/6/art/opuscula_math_4340.pdfpathpartition |
| spellingShingle | Mekkia Kouider Mohamed Zamime On the path partition of graphs Opuscula Mathematica path partition |
| title | On the path partition of graphs |
| title_full | On the path partition of graphs |
| title_fullStr | On the path partition of graphs |
| title_full_unstemmed | On the path partition of graphs |
| title_short | On the path partition of graphs |
| title_sort | on the path partition of graphs |
| topic | path partition |
| url | https://www.opuscula.agh.edu.pl/vol43/6/art/opuscula_math_4340.pdf |
| work_keys_str_mv | AT mekkiakouider onthepathpartitionofgraphs AT mohamedzamime onthepathpartitionofgraphs |