Graphs in r

To any two graphs G and H one can associate a cell complex Hom (G, H) by taking all graph multihomomorphisms from G to H as cells. In this paper we prove the Lov´sz conjecture which states that a if Hom (C2r+1 , G) is k-connected, then χ(G) ≥ k + 4, where r, k ∈ Z, r ≥ 1, k ≥ −1, and C2r+1 denotes the cycle with 2r +1 vertices. The proof requires analysis of the complexes Hom (C2r+1 , Kn ). For even n, the obstructions to graph colorings are provided by the presence of torsion...

44p noel_noel 17-01-2013 58 8   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Rainbow matchings in r-partite r-graphs...

9p thulanh8 19-09-2011 41 2   Download

Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: A Rainbow k-Matching in the Complete Graph with r Colors...

13p thulanh8 17-09-2011 39 4   Download

It is shown that if a d-regular graph contains s vertices so that the distance between any pair is at least 4k, then its adjacency matrix has at least s eigenvalues which are at least 2pd − 1 cos(  2k ). A similar result has been proved by Friedman using more sophisticated tools.More generally, Serre has shown (see [3], [4] ) that for any fixed r and for any infinite family of d-regular graphs Gi, lim inf r(Gi) 2pd − 1. The same result has been proved by Friedman already in [5].

4p thulanh5 12-09-2011 97 6   Download