Packing of three copies of a digraph into the transitive tournament

2004 ◽  
Vol 24 (3) ◽  
pp. 443 ◽  
Author(s):  
Monika Pilśniak
Keyword(s):  
Transitive Tournament

scholarly journals Turán theorems for unavoidable patterns

2021 ◽  
pp. 1-20
Author(s):  
ANTÓNIO GIRÃO ◽  
BHARGAV NARAYANAN
Keyword(s):  
Complete Graph ◽  
Blow Up ◽  
Ramsey Numbers ◽  
Order Of Magnitude ◽  
Transitive Tournament ◽  
Unavoidable Patterns

Abstract We prove Turán-type theorems for two related Ramsey problems raised by Bollobás and by Fox and Sudakov. First, for t ≥ 3, we show that any two-colouring of the complete graph on n vertices that is δ-far from being monochromatic contains an unavoidable t-colouring when δ ≫ n−1/t, where an unavoidable t-colouring is any two-colouring of a clique of order 2t in which one colour forms either a clique of order t or two disjoint cliques of order t. Next, for t ≥ 3, we show that any tournament on n vertices that is δ-far from being transitive contains an unavoidable t-tournament when δ ≫ n−1/[t/2], where an unavoidable t-tournament is the blow-up of a cyclic triangle obtained by replacing each vertex of the triangle by a transitive tournament of order t. Conditional on a well-known conjecture about bipartite Turán numbers, both our results are sharp up to implied constants and hence determine the order of magnitude of the corresponding off-diagonal Ramsey numbers.

scholarly journals ∗-graphs of vertices of the generalized transitive tournament polytope

1998 ◽  
Vol 179 (1-3) ◽  
pp. 49-57 ◽  
Author(s):  
Alberto Borobia ◽  
Valerio Chumillas
Keyword(s):  
Transitive Tournament

scholarly journals Packing of two digraphs into a transitive tournament

2007 ◽  
Vol 307 (7-8) ◽  
pp. 971-974 ◽  
Author(s):  
Monika Pilśniak
Keyword(s):  
Transitive Tournament

scholarly journals Vertices of the generalized transitive tournament polytype

1997 ◽  
Vol 163 (1-3) ◽  
pp. 229-234 ◽  
Author(s):  
Alberto Borobia
Keyword(s):  
Transitive Tournament

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

10.37236/6521 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Pierre Aboulker ◽  
Nathann Cohen ◽  
Frédéric Havet ◽  
William Lochet ◽  
Phablo F. S. Moura ◽  
...  
Keyword(s):  
Directed Path ◽  
Directed Paths ◽  
Oriented Path ◽  
Transitive Tournament ◽  
Dichromatic Number

In 1985, Mader conjectured the existence of a function $f$ such that every digraph with minimum out-degree at least $f(k)$ contains a subdivision of the transitive tournament of order $k$. This conjecture is still completely open, as the existence of $f(5)$ remains unknown. In this paper, we show that if $D$ is an oriented path, or an in-arborescence (i.e., a tree with all edges oriented towards the root) or the union of two directed paths from $x$ to $y$ and a directed path from $y$ to $x$, then every digraph with minimum out-degree large enough contains a subdivision of $D$. Additionally, we study Mader's conjecture considering another graph parameter. The dichromatic number of a digraph $D$ is the smallest integer $k$ such that $D$ can be partitioned into $k$ acyclic subdigraphs. We show that any digraph with dichromatic number greater than $4^m (n-1)$ contains every digraph with $n$ vertices and $m$ arcs as a subdivision. We show that any digraph with dichromatic number greater than $4^m (n-1)$ contains every digraph with $n$ vertices and $m$ arcs as a subdivision.

scholarly journals Transitive Tournament Tilings in Oriented Graphs with Large Minimum Total Degree

2021 ◽  
Vol 35 (1) ◽  
pp. 250-266
Author(s):  
Louis DeBiasio ◽  
Allan Lo ◽  
Theodore Molla ◽  
Andrew Treglown
Keyword(s):  
Total Degree ◽  
Oriented Graphs ◽  
Transitive Tournament

scholarly journals Short Score Certificates for Upset Tournaments

10.37236/1362 ◽  
1998 ◽  
Vol 5 (1) ◽  
Author(s):  
Jeffrey L. Poet ◽  
Bryan L. Shader
Keyword(s):  
Lower Bounds ◽  
Upper Bounds ◽  
General Construction ◽  
Transitive Tournament ◽  
One To One

A score certificate for a tournament, $T$, is a collection of arcs of $T$ which can be uniquely completed to a tournament with the same score-list as $T$'s, and the score certificate number of $T$ is the least number of arcs in a score certificate of $T$. Upper bounds on the score certificate number of upset tournaments are derived. The upset tournaments on $n$ vertices are in one–to–one correspondence with the ordered partitions of $n-3$, and are "almost" transitive tournaments. For each upset tournament on $n$ vertices a general construction of a score certificate with at most $2n-3$ arcs is given. Also, for the upset tournament, $T_{\lambda}$, corresponding to the ordered partition $\lambda$, a score certificate with at most $n+2k+3$ arcs is constructed, where $k$ is the number of parts of $\lambda$ of size at least 2. Lower bounds on the score certificate number of $T_{\lambda}$ in the case that each part is sufficiently large are derived. In particular, the score certificate number of the so-called nearly transitive tournament on $n$ vertices is shown to be $n+3$, for $n\geq 10$.

Sign in / Sign up

Export Citation Format

Share Document