Sandi Klavžar is an associate editor of Discrete Applied Mathematics and Ars Mathematica Contemporanea, advisory editor of Discussiones Mathematicae Graph Theory, editor of the Bulletin of the Malaysian Mathematical Society and is a member of editorial boards of other journals including Asian-European Journal of Mathematics, European Journal of Combinatorics, Graphs & Combinatorics, MATCH Communications in Mathematical and in Computer Chemistry. Boštjan Brešar is a member of the editorial board of Discrete Mathematics & Theoretical Computer Science and was a guest editor of Discrete Applied Mathematics and and Discussiones Mathematicae Graph Theory.
C.04 Editorial board of an international magazine
COBISS.SI-ID: 25342464Invited plenary lecture at the International Conference on Mathematical Computer Engineering (ICMCE-2017), VIT University, Chennai, India, 3-4 Nov., 2017.
B.04 Guest lecture
COBISS.SI-ID: 18158937We study isometric subgraphs found in hypercubes, called partial cubes. We focus on three aspects: understanding the cycle space of such subgraphs, exploring established subfamilies and properties, and finding symmetric ones. As we show, convex cycles in partial cubes have many intriguing properties, from spanning a simply connected space to forming complex substructures such as intertwinings and traverses. We analyze partial cubes with high girth to obtain results on the structure and degree of such graphs. This knowledge is transferred to symmetric partial cubes to obtain a complete classification of cubic, vertex-transitive ones and to find a connection between partial cubes having mirror automorphisms and finite Coxeter groups. We study various subfamilies of partial cubes to expose a connection between (pseudo-) hyperplane arrangements, antipodal subgraphs, oriented matroids, median graphs, and many other structures found in partial cubes. With our main tool, the concept of partial cube minors, we create a map of partial cubes determining the hierarchical structure of subfamilies of partial cubes, and providing new characterizations and generalizations. Lastly, computational and enumerative properties of partial cubes bounded by their isometric dimension are discussed, together with a result showing that finding isomorphisms of graphs is GI-complete already for one of the simplest classes of partial cubes: median graphs.
D.09 Tutoring for postgraduate students
COBISS.SI-ID: 18363993