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Projects / Programmes source: ARIS

Topological and metric graph theory

Research activity

Code Science Field Subfield
1.01.00  Natural sciences and mathematics  Mathematics   

Code Science Field
P110  Natural sciences and mathematics  Mathematical logic, set theory, combinatories 
Keywords
graph, embedding, genus, edge-width, face-width, crossing number, minor, coloring, nowhere-zero flow, distance, convexity, discrete metric space, Cartesian product, direct product, median graph, partial cube, isometric subgraph, automorphism
Evaluation (rules)
source: COBISS
Researchers (25)
no. Code Name and surname Research area Role Period No. of publicationsNo. of publications
1.  23201  PhD Iztok Banič  Mathematics  Researcher  2004 - 2007  185 
2.  22402  PhD Drago Bokal  Mathematics  Junior researcher  2004 - 2007  238 
3.  17005  PhD Boštjan Brešar  Mathematics  Researcher  2004 - 2007  403 
4.  25993  PhD Sergio Cabello Justo  Mathematics  Researcher  2005 - 2007  218 
5.  15313  MSc Igor Đukanović  Mathematics  Researcher  2005 - 2007  29 
6.  16332  PhD Gašper Fijavž  Mathematics  Researcher  2004 - 2007  121 
7.  24751  PhD Janja Jerebic  Administrative and organisational sciences  Researcher  2005 - 2007  116 
8.  11220  PhD Martin Juvan  Mathematics  Researcher  2004 - 2007  235 
9.  05949  PhD Sandi Klavžar  Mathematics  Researcher  2004 - 2007  1,175 
10.  25571  PhD Matjaž Kovše  Mathematics  Junior researcher  2005 - 2007  77 
11.  03425  PhD Jernej Kozak  Mathematics  Researcher  2004  296 
12.  13351  PhD Alenka Lipovec  Educational studies  Researcher  2004 - 2007  512 
13.  13429  MSc Jože Marinček  Mathematics  Researcher  2004 - 2007  29 
14.  08727  PhD Uroš Milutinović  Mathematics  Researcher  2004 - 2007  348 
15.  01931  PhD Bojan Mohar  Mathematics  Head  2004 - 2007  1,002 
16.  09634  PhD Bojan Orel  Mathematics  Researcher  2004  124 
17.  20839  PhD Iztok Peterin  Mathematics  Researcher  2004 - 2007  350 
18.  22649  PhD Janez Povh  Computer intensive methods and applications  Researcher  2004 - 2007  341 
19.  15518  PhD Riste Škrekovski  Mathematics  Researcher  2004 - 2007  506 
20.  24904  PhD Simon Špacapan  Mathematics  Researcher  2005 - 2007  109 
21.  21821  PhD Andrej Taranenko  Mathematics  Researcher  2006 - 2007  130 
22.  11666  PhD Aleksander Vesel  Computer intensive methods and applications  Researcher  2004 - 2007  338 
23.  24049  PhD Andrej Vodopivec  Mathematics  Junior researcher  2004 - 2007  14 
24.  19886  PhD Emil Žagar  Mathematics  Researcher  2004  186 
25.  18504  PhD Petra Žigert Pleteršek  Mathematics  Researcher  2004 - 2007  174 
Organisations (1)
no. Code Research organisation City Registration number No. of publicationsNo. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  19,658 
Abstract
The first part of the project we shall primarily consider properties of embedded graphs. In particular, we will investigate locally planar embeddings with special emphasis on edge-width, face-width and their generalization - the nonseparating width. In connection to the theory of graph minors we shall pay our interest towards crossing number of graphs, unavoidable structures in large graphs, and forbidden minor characterizations of certain minor closed graph classes. We shall also study spectral properties of (embedded) graphs with respect to the discrete Laplacian operator. Further, we shall investigate graph colorings, in particular list colorings, circular chromatic number, and nowhere-zero flows in graphs. In the second part of the project we shall investigate classes of graphs that are defined by metric properties or for which there exists a factorization with respect to graph products. Factorizations of hypercubes with respect to the direct product will be studied, as well as conditions under which this kind of factorization could be generalized to Cartesian product graphs and median graphs. We shall study partial cubes, their subclasses related to median graphs, and the subclass of regular partial cubes. In relation with the graceful trees conjecture we shall introduce a new labeling of partial cubes and study the question whether all partial cubes admit the generalized graceful labeling. Cube polynomial for median graphs will be further investigated, and relations between the zeros of this polynomial and important classes of median graphs will be considered. We shall study graph invariants of graph products, in particular the multiple domination, and investigate relations of obtained results with the Vizing conjecture on domination number of Cartesian product graphs.
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