Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, June 07, 2007, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Hossein Hajiabolhassan (Shahid Beheshti Univ., Tehran)

Graphs homomorphisms and spectral conditions

In this talk we review some algebraic no-homomorphism theorems [1, 2, 3, 4, 5]. In this approach we consider the combinatorial Laplacian and co-Laplacian as well as the adjacency matrix and we introduce necessary conditions for the existence of graph homomorphisms in terms of their spectra. To show the applicability of the general results, as a couple of examples, we present some applications in graph decompositions, circular chromatic number and fractional chromatic number. Next, by applying nodal domain theory, we show how one can consider the sign-graphs of the corresponding eigenfunctions to obtain no-homomorphism criteria.

References:

[1] A. Daneshgar and H. Hajiabolhassan, Graph homomorphisms through random walks, Journal of Graph Theory 44 (2003), 15-38.
[2] A. Daneshgar and H. Hajiabolhassan, Random walks and Graph homomorphisms, Morphisms and Statistical Physics, J. Nešetřil and P. Winkler Eds., AMS Proceedings DIMACS Series, 63 (2004), 49-64.
[3] A. Daneshgar and H. Hajiabolhassan, Graph homomorphisms and nodal domains, Linear Algebra and Its Applications, 418 (2006), 44-52.
[4] A. Daneshgar and H. Hajiabolhassan, Circular chromatic number and algebraic no-homomorphism theorems, European Journal of Combinatorics, to appear.
[5] A. Daneshgar and H. Hajiabolhassan, On the isoperimetric spectrum of graphs, manuscript 2007.

Talk announcement in [PDF].


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