Bispindles in Strongly Connected Digraphs with Large Chromatic Number

Bispindle in strongly connected digraphs with large chromatic number

A (k1 + k2)-bispindle is the union of k1 (x, y)-dipaths and k2 (y, x)-dipaths, all these dipaths being pairwise internally disjoint. Recently, Cohen et al. showed that for every (1, 1)bispindle B, there exists an integer k such that every strongly connected digraph with chromatic number greater than k contains a subdivision of B. We investigate generalisations of this result by first showing co...

On spectral radius of strongly connected digraphs

 It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.  

The number of h-strongly connected digraphs with small diameter

Let D s (n; h, d = k) denote the number of h-strongly connected digraphs of order n and diameter equal to k. In this paper it is shown that: i) Ds(n; 11" d = 3) = 4(~) (3/4 + o(I))n for every fixed h ;::: 1; ii) Ds(n; h, d = 4) = 4(~) (2h 2 + 2-2 + o(I))n for every fixed h ;::: 2; iii) Ds(n; 11" d = k) = 4(~) ((2h+l I)2-kh+:3h-2 + o(I))n for every fixed h ;::: 1 and k ;::: 5. Similar asymptotic...

Subdivisions of oriented cycles in digraphs with large chromatic number

Strongly Connected Multivariate Digraphs

Generalizing the idea of viewing a digraph as a model of a linear map, we suggest a multi-variable analogue of a digraph, called a hydra, as a model of a multi-linear map. Walks in digraphs correspond to usual matrix multiplication while walks in hydras correspond to the tensor multiplication introduced by Robert Grone in 1987. By viewing matrix multiplication as a special case of this tensor m...