Naslov: | A note on acyclic number of planar graphs |
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Avtorji: | ID Petruševski, Mirko (Avtor) ID Škrekovski, Riste (Avtor) |
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: | 975 |
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Število prenosov: | 16 |
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