| Naslov: | A note on acyclic number of planar graphs |
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| Avtorji: | ID Petruševski, Mirko (Avtor)
ID Škrekovski, Riste (Avtor) |
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| Datoteke: |  RAZ_Petrusevski_Mirko_i2017.pdf (227,50 KB)
MD5: 16221246B7AECF9331577AC35E4236C8
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| Jezik: | Angleški jezik |
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| Vrsta gradiva: | Neznano |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: | ZUP - Založba Univerze na Primorskem
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| Opis: | 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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| Ključne besede: | induced forest, acyclic number, planar graph, girth |
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| Leto izida: | 2017 |
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| Št. strani: | str. 317-322 |
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| Številčenje: | Vol. 13, no. 2 |
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| PID: | 20.500.12556/RUP-17628  |
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| UDK: | 519.17 |
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| ISSN pri članku: | 1855-3966 |
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| COBISS.SI-ID: | 2048439059 |
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| Datum objave v RUP: | 03.01.2022 |
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| Število ogledov: | 2106 |
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| Število prenosov: | 22 |
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| Metapodatki: |    |
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