Báo cáo toán học: "Colouring 4-cycle systems with specified block colour patterns: the case of embedding P3-designs" ppsx
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...
Báo cáo toán học: "On edge colorings with at least q colors in every subset of p vertices" ppsx
... 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...
Báo cáo toán học: "A simple Havel–Hakimi type algorithm to realize graphical degree sequences of directed graphs" ppsx
... 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...
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