| 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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