منابع مشابه
On the girth of digraphs
It was conjectured by Caccetta and H aggkvist in 1978 that the girth of every digraph with n vertices and minimum outdegree r is at most dn=re. The conjecture was proved for r = 2 by Caccetta and H aggkvist, for r = 3 by Hamidoune and for r = 4; 5 by Ho ang and Reed. In this paper, the following two main results are proved: 1. The diameter of every strongly connected digraph of order n with g...
متن کاملUniquely D-colourable Digraphs with Large Girth
Let C and D be digraphs. A mapping f : V (D) → V (C) is a Ccolouring if for every arc uv of D, either f(u)f(v) is an arc of C or f(u) = f(v), and the preimage of every vertex of C induces an acyclic subdigraph in D. We say that D is C-colourable if it admits a C-colouring and that D is uniquely Ccolourable if it is surjectively C-colourable and any two C-colourings of D differ by an automorphis...
متن کاملWeakly Distance-Regular Digraphs of Girth 2
In this paper, we give two constructions of weakly distance-regular digraphs of girth 2, and prove that certain quotient digraph of a commutative weakly distancetransitive digraph of girth 2 is a distance-transitive graph. As an application of the result, we not only give some constructions of weakly distance-regular digraphs which are not weakly distance-transitive, but determine a special cla...
متن کاملTitle : A Family of Weakly Distance - Regular Digraphs of Girth
All weakly distance-regular digraphs with girth $2$ and k-k_{1,1}=1 are classified. A Family of Weakly Distance-Regular Digraphs of Girth 2 Kaishun Wang∗ School of Mathematical Sciences Beijing Normal University Beijing 100875, P.R. China Abstract All weakly distance-regular digraphs with girth 2 and k − k1,1 = 1 are classified.All weakly distance-regular digraphs with girth 2 and k − k1,1 = 1 ...
متن کاملStrengthened Brooks' Theorem for Digraphs of Girth at least Three
Brooks’ Theorem states that a connected graph G of maximum degree ∆ has chromatic number at most ∆, unless G is an odd cycle or a complete graph. A result of Johansson shows that if G is triangle-free, then the chromatic number drops to O(∆/ log∆). In this paper, we derive a weak analog for the chromatic number of digraphs. We show that every (loopless) digraph D without directed cycles of leng...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 1980
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.3190040311