1. On the connectivity of bipartite distancebalanced graphsŠtefko Miklavič, Primož Šparl, 2012, original scientific article Abstract: A connected graph ▫$\varGamma$▫ is said to be distancebalanced whenever for any pair of adjacent vertices ▫$u,v$▫ of ▫$\varGamma$▫ the number of vertices closer to ▫$u$▫ than to ▫$v$▫ is equal to the number of vertices closer to ▫$v$▫ than to ▫$u$▫. In [K. Handa, Bipartite graphs with balanced ▫$(a,b)$▫partitions, Ars Combin. 51 (1999), 113119] Handa asked whether every bipartite distancebalanced graph, that is not a cycle, is 3connected. In this paper the Handa question is answered in the negative. Moreover, we show that a minimal bipartite distancebalanced graph, that is not a cycle and is not 3connected, has 18 vertices and is unique. In addition, we give a complete classification of non3connected bipartite distancebalanced graphs for which the minimal distance between two vertices in a 2cut is three. All such graphs are regular and for each ▫$k \geq 3$▫ there exists an infinite family of such graphs which are ▫$k$▫regular.Furthermore, we determine a number of structural properties that a bipartite distancebalanced graph, which is not 3connected, must have. As an application, we give a positive answer to the Handa question for the subfamily of bipartite strongly distancebalanced graphs. Found in: ključnih besedah Summary of found: Zadetek v naslovu Keywords: graph theory, connected graphs, connectivity, distancebalanced graphs, bipartite graphs Published: 15.10.2013; Views: 1346; Downloads: 50 Full text (0,00 KB) 
2. Maximum genus, connectivity, and Nebeský's theoremMartin Škoviera, Roman Nedela, Dan Steven Archdeacon, Michal Kotrbčík, 2015, original scientific article Found in: ključnih besedah Summary of found: Zadetek v naslovu Keywords: maksimalen rod, Nebeskýnov rod, Bettijevo število, povezanost, maximum genus, Nebeský theorem, Betti number, connectivity Published: 15.10.2015; Views: 1083; Downloads: 68 Full text (0,00 KB) 
3. Vector connectivity in graphsFerdinando Cicalese, Martin Milanič, Pinar Heggernes, Endre Boros, Pim Van 't Hof, Romeo Rizzi, 2014, published scientific conference contribution abstract (invited lecture) Found in: ključnih besedah Summary of found: Zadetek v naslovu Keywords: vektorska povezanost, aproksimacijski algoritmi, polinomski algoritmi, NPpoln problem, razcepljeni grafi, kografi, drevesa, vector connectivity, approximation algorithms, poynomial time algorithms, NPhard problem, split graphs, cographs, trees Published: 15.10.2015; Views: 1315; Downloads: 96 Full text (0,00 KB) This document has more files! More...

4. On cyclic edgeconnectivity of fullerenesDragan Marušič, Klavdija Kutnar, 2008, original scientific article Abstract: A graph is said to be cyclically ▫$k$▫edgeconnected, if at least ▫$k$▫ edges must be removed to disconnect it into two components, each containing a cycle. Such a set of ▫$k$▫ edges is called a cyclickedge cutset and it is called a trivial cyclickedge cutset if at least one of the resulting two components induces a single ▫$k$▫cycle. It is known that fullerenes, that is, 3connected cubic planar graphs all of whose faces are pentagons and hexagons, are cyclically 5edgeconnected. In this article it is shown that a fullerene ▫$F$▫ containing a nontrivial cyclic5edge cutset admits two antipodal pentacaps, that is, two antipodal pentagonal faces whose neighboring faces are also pentagonal. Moreover, it is shown that ▫$F$▫ has a Hamilton cycle, and as a consequence at least ▫$15 \cdot 2^{n/201/2}$▫ perfect matchings, where ▫$n$▫ is the order of ▫$F$▫. Found in: ključnih besedah Summary of found: Zadetek v naslovu Keywords: graph, fullerene graph, cyclic edgeconnectivity, hamilton cycle, perfect matching Published: 03.04.2017; Views: 705; Downloads: 83 Full text (0,00 KB) 
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6. The price of connectivity for cycle transversalsTatiana R. Hartinger, Matthew Johnson, Martin Milanič, Daniël Paulusma, 2015, published scientific conference contribution Found in: ključnih besedah Summary of found: Zadetek v naslovu Keywords: price of connectivity, hereditary graph class, path, cycle, transversal Published: 08.08.2016; Views: 1375; Downloads: 40 Full text (0,00 KB) 
7. The price of connectivity for cycle transversalsTatiana R. Hartinger, Matthew Johnson, Martin Milanič, Daniël Paulusma, 2016, original scientific article Found in: ključnih besedah Summary of found: Zadetek v naslovu Keywords: price of connectivity, hereditary graph class, path, cycle, transversal Published: 08.08.2016; Views: 838; Downloads: 36 Full text (0,00 KB) 
8. Nove karakterizacije v strukturni teoriji grafovTatiana Romina Hartinger, 2017, doctoral dissertation Found in: ključnih besedah Summary of found: ...product, direct product, strong product, price of connectivity, cycle transversal, path transversal... Keywords: 1perfectly orientable graph, structural characterization of families of graphs, chordal graph, interval graph, circular arc graph, cograph, blockcactus graph, cobipartite graph, K4minorfree graph, outerplanar graph, graph product, Cartesian product, lexicographic product, direct product, strong product, price of connectivity, cycle transversal, path transversal Published: 09.11.2017; Views: 580; Downloads: 10 Full text (0,00 KB) 
9. Aproksimacijski vidiki vektorske dominacije in vektorske povezanosti v grahMirza Krbezlija, 2018, undergraduate thesis Found in: ključnih besedah Summary of found: ...graph, vector domination, vector connectivity, submodular set covering problem, approximation algorithm, greedy... Keywords: graph, vector domination, vector connectivity, submodular set covering problem, approximation algorithm, greedy heuristic, integer linear programming Published: 17.09.2018; Views: 330; Downloads: 11 Full text (0,00 KB) 