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2. A note on acyclic number of planar graphsMirko 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 Full text (227,50 KB) |
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4. Beasley, LeRoy B., Kang, Kyung-Tae, Song, Seok-Zun: Isolation numbers of integer matrices and their preservers. (English summary). - Bull. Korean Math. Soc. 57 (2020), no. 3, 535-545Marko Orel, 2021, review, book review, critique Keywords: preserver problems, matrices with nonnegative coefficients, isolation number Published in RUP: 06.05.2021; Views: 732; Downloads: 7 Link to full text |
5. On the balanced upper chromatic number of finite projective planesZoltán L. Blázsik, Aart Blokhuis, Štefko Miklavič, Zoltán Lóránt Nagy, Tamás Szőnyi, 2021, original scientific article Keywords: projective planes, balanced upper chromatic number, difference sets, planar functions, probabilistic method Published in RUP: 18.01.2021; Views: 962; Downloads: 35 Link to full text |
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