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A note on acyclic number of planar graphs
Mirko Petruševski, Riste Škrekovski, 2017, izvirni znanstveni članek

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.
Ključne besede: induced forest, acyclic number, planar graph, girth
Objavljeno v RUP: 03.01.2022; Ogledov: 895; Prenosov: 16
.pdf Celotno besedilo (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, objavljeni znanstveni prispevek na konferenci

Ključne besede: graph class, treewidth, clique number
Objavljeno v RUP: 10.11.2020; Ogledov: 1260; Prenosov: 34
URL Povezava na celotno besedilo

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