Bispindle in strongly connected digraphs with large chromatic number

  title={Bispindle in strongly connected digraphs with large chromatic number},
  author={Nathann Cohen and Fr{\'e}d{\'e}ric Havet and William Lochet and Raul Lopes},
  journal={Electron. Notes Discret. Math.},

Remarks on the subdivisions of bispindles and two-blocks cycles in highly chromatic digraphs

A $(2+1)$-bispindle $B(k_1,k_2;k_3)$ is the union of two $xy$-dipaths of respective lengths $k_1$ and $k_2$, and one $yx$-dipath of length $k_3$, all these dipaths being pairwise internally disjoint.

Sous-structures dans les graphes dirigés

Le but principal de cette these est de presenter des conditions suffisantes pour garantir l'existence de subdivisions dans les graphes diriges. Bien que ce genre de questions soit assez bien maitrise



Subdivisions in Digraphs of Large Out-Degree or Large Dichromatic Number

If $D$ is an oriented path, or an in-arborescence, or the union of two directed paths from x to y and a directed path from y tox, then every digraph with minimum out-degree large enough contains a subdivision of $D$.

Cycles with two blocks in k‐chromatic digraphs

This paper is able to find a digraph which shows that the answer to the above problem is no and it is shown that if in addition £D is Hamiltonian, then its underlying simple graph is $(k+\ell-1)$-degenerate and thus the chromatic number of $D$ is at most $k-\ell$, which is tight.

Antidirected Subtrees of Directed Graphs

  • S. Burr
  • Mathematics
    Canadian Mathematical Bulletin
  • 1982
The purpose of this paper is to prove the following result: Theorem. Let T be a directed tree with k arcs and with no directed path of length 2. Then if G is any directed graph with n points and at

Subdivisions of oriented cycles in digraphs with large chromatic number

It is shown that for any oriented cycle C, there are digraphs containing no subdivision of $C$ (as a subdigraph) and arbitrarily large chromatic number and for any cycle with two blocks, every strongly connected digraph with sufficiently large Chromatic number contains a subdivision of C.


A well-known theorem of Ramsay (8; 9) states that to every n there exists a smallest integer g(n) so that every graph of g(n) vertices contains either a set of n independent points or a complete

Graphs with k odd cycle lengths

Subtrees of directed graphs and hypergraphs.