Báo cáo toán học: "Colouring 4-cycle systems with specified block colour patterns: the case of embedding P3-designs" ppsx

... that the existence of a 4-cycle system of order n having an m-colouring of type bd, implies the one of a 4-cycle system of order n + 8 having an (m + 1)-colouring of type bd. ✷ 4 2-Colouring of ... , n+3 4 } there is a 4-cycle system of order n with a proper m-colouring of type bf . Proof.Thecasesm =3andm = n+3 4 are proved by using Theorem 2.3 and Theorem 2.4 re...

Ngày tải lên: 07/08/2014, 06:22

... consider the 2a i+1 vertices in V (M  i+1 ) and the edges of M i incident to these vertices. We have four cases. Case 1: If 2a i+1 = a i (so we have the first case in (3)), then this is M  i . Case ... concepts see the monograph of Bollob´as [1]. V (G)andE(G)denotethe vertex-set and the edge-set of the graph G. K n is the complete graph on n vertices. In this paper...

Ngày tải lên: 07/08/2014, 07:21

Ngày tải lên: 05/08/2014, 15:21

... step. After the last step we find that the sequence reduced by C is graphical.  Proof of Theorem 2: We can easily achieve now the required graphical realization of (d + , d − ) if we use Lemma 6 with the ... of the complete graph G, but their proof was independent of Tutte’s proof and they referred to Havel’s theorem. In 1962 S.L. Hakimi studied the degree sequence probl...

Ngày tải lên: 08/08/2014, 12:22

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:21