1. |
2. A note on acyclic number of planar graphsMirko 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 Celotno besedilo (227,50 KB) |
3. |
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, recenzija, prikaz knjige, kritika Ključne besede: preserver problems, matrices with nonnegative coefficients, isolation number Objavljeno v RUP: 06.05.2021; Ogledov: 732; Prenosov: 7 Povezava na celotno besedilo |
5. On the balanced upper chromatic number of finite projective planesZoltán L. Blázsik, Aart Blokhuis, Štefko Miklavič, Zoltán Lóránt Nagy, Tamás Szőnyi, 2021, izvirni znanstveni članek Ključne besede: projective planes, balanced upper chromatic number, difference sets, planar functions, probabilistic method Objavljeno v RUP: 18.01.2021; Ogledov: 962; Prenosov: 35 Povezava na celotno besedilo |
6. |
7. |
8. |
9. |
10. |