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A note on acyclic number of planar graphs
Mirko Petruševski, Riste Škrekovski, 2017, original scientific article

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.
Keywords: induced forest, acyclic number, planar graph, girth
Published in RUP: 03.01.2022; Views: 895; Downloads: 16
.pdf Full text (227,50 KB)

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Treewidth versus clique number in graph classes with a forbidden structure
Clément Jean Dallard, Martin Milanič, Kenny Štorgel, 2020, published scientific conference contribution

Keywords: graph class, treewidth, clique number
Published in RUP: 10.11.2020; Views: 1260; Downloads: 34
URL Link to full text

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Vložitev ne-ravninskih grafov : hramba in predstavitev
Đorđe Klisura, 2020, undergraduate thesis

Keywords: planar graph, graph representation, crossing number, graph database
Published in RUP: 02.10.2020; Views: 1088; Downloads: 12
URL Link to full text

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