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1.
On girth-biregular graphs
György Kiss, Štefko Miklavič, Tamás Szőnyi, 2023, original scientific article

Keywords: girth cycle, girth-biregular graph, steiner system, generalized polygons
Published in RUP: 06.11.2023; Views: 229; Downloads: 3
.pdf Full text (429,83 KB)

2.
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: 885; Downloads: 16
.pdf Full text (227,50 KB)

3.
Extremal edge-girth-regular graphs
Ajda Zavrtanik Drglin, Slobodan Filipovski, Robert Jajcay, Tom Raiman, 2021, original scientific article

Keywords: regular graph, girth, vertex-transitive graph
Published in RUP: 16.07.2021; Views: 963; Downloads: 27
URL Link to full text

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Edge-girth-regular graphs
Robert Jajcay, György Kiss, Štefko Miklavič, 2018, original scientific article

Keywords: girth, edge-regular graph, edge-girth-regular graph
Published in RUP: 18.05.2018; Views: 2024; Downloads: 371
URL Link to full text

7.
Biregular cages of odd girth
Geoffrey Exoo, Robert Jajcay, 2016, original scientific article

Keywords: cage, biregular cage, recursive construction, girth
Published in RUP: 08.08.2016; Views: 2565; Downloads: 174
URL Link to full text

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A complete classification of cubic symmetric graphs of girth 6
Klavdija Kutnar, Dragan Marušič, 2009, original scientific article

Abstract: A complete classification of cubic symmetric graphs of girth 6 is given. It is shown that with the exception of the Heawood graph, the Moebius-Kantor graph, the Pappus graph, and the Desargues graph, a cubic symmetric graph ▫$X$▫ of girth 6 is a normal Cayley graph of a generalized dihedral group; in particular, (i) ▫$X$▫ is 2-regular if and only if it is isomorphic to a so-called ▫$I_k^n$▫-path, a graph of order either ▫$n^2/2$▫ or ▫$n^2/6$▫, which is characterized by the fact that its quotient relative to a certain semiregular automorphism is a path. (ii) ▫$X$▫ is 1-regular if and only if there exists an integer ▫$r$▫ with prime decomposition ▫$r=3^s p_1^{e_1} \dots p_t^{e_t} > 3$▫, where ▫$s \in \{0,1\}$▫, ▫$t \ge 1$▫, and ▫$p_i \equiv 1 \pmod{3}$▫, such that ▫$X$▫ is isomorphic either to a Cayley graph of a dihedral group ▫$D_{2r}$▫ of order ▫$2r$▫ or ▫$X$▫ is isomorphic to a certain ▫$\ZZ_r$▫-cover of one of the following graphs: the cube ▫$Q_3$▫, the Pappus graph or an ▫$I_k^n(t)$▫-path of order ▫$n^2/2$▫.
Keywords: graph theory, cubic graphs, symmetric graphs, ▫$s$▫-regular graphs, girth, consistent cycle
Published in RUP: 15.10.2013; Views: 3912; Downloads: 86
URL Link to full text

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