| Title: | A note on acyclic number of planar graphs |
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| Authors: | ID Petruševski, Mirko (Author)
ID Škrekovski, Riste (Author) |
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| Files: |  RAZ_Petrusevski_Mirko_i2017.pdf (227,50 KB)
MD5: 16221246B7AECF9331577AC35E4236C8
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| Language: | English |
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| Work type: | Unknown |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | The acyclic number ▫$a(G)$▫ of a graph ▫$G$▫ is the maximum order of an induced forest in ▫$G$▫. The purpose of this short paper is to propose a conjecture that ▫$a(G)\geq \left( 1-\frac{3}{2g}\right)n$▫ holds for every planar graph ▫$G$▫ of girth ▫$g$▫ and order ▫$n$▫, which captures three known conjectures on the topic. In support of this conjecture, we prove a weaker result that ▫$a(G)\geq \left( 1-\frac{3}{g} \right)n$▫ holds. In addition, we give a construction showing that the constant ▫$\frac{3}{2}$▫ from the conjecture cannot be decreased. |
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| Keywords: | induced forest, acyclic number, planar graph, girth |
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| Year of publishing: | 2017 |
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| Number of pages: | str. 317-322 |
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| Numbering: | Vol. 13, no. 2 |
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| PID: | 20.500.12556/RUP-17628  |
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| UDC: | 519.17 |
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| ISSN on article: | 1855-3966 |
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| COBISS.SI-ID: | 2048439059 |
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| Publication date in RUP: | 03.01.2022 |
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| Views: | 2115 |
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| Downloads: | 22 |
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