Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options not deleted user 17798

A directed graph is a graph with directed edges. Loops and 2-cycles are usually allowed. See also the tag *quiver*.

2 votes

Does a strong digraph always admit a vertex that lies on some path between $\Theta(n^2)$ pai...

I don't have an answer, but I do have an idea for how a proof could go. I would make this a comment, but it is too long. (i) Prove that every 2-strongly connected digraph (i.e. remains strongly conne …
Louis D's user avatar
  • 1,701
4 votes

A counterexample to a conjecture of Nash-Williams about hamiltonicity of digraphs?

I realize this question was asked seven years ago and hasn't had a comment in four years, but I just came across it and thought it might be worth sharing what I've learned. As @HughThomas mentions, si …
Louis D's user avatar
  • 1,701
1 vote

Proving that every strongly connected tournament T on at least 4 vertices contains distinct ...

After reading relep's answer I revisited the problem and came up with a different fairly simple proof for Question 1, but before I get to that, I recently found that this problem has a long history al …
Louis D's user avatar
  • 1,701
3 votes
2 answers
2k views

Proving that every strongly connected tournament T on at least 4 vertices contains distinct ...

I have a two part question: Is there a simple proof that every strongly connected tournament $T$ on $n\geq 4$ vertices contains distinct $u,v\in V(T)$ such that $T-u$ and $T-v$ are strongly connected …
Louis D's user avatar
  • 1,701
4 votes
1 answer
267 views

Dominating sets in subtournaments of the Paley tournament

For a tournament $T$, let $\mathrm{dom}(T)$ be the order of a smallest dominating set in $T$. Let $q$ be a prime power congruent to 3 mod 4 and let $T_q$ be the Paley tournament on $q$ vertices. Is i …
Louis D's user avatar
  • 1,701
1 vote

Directed version of this lemma

Regarding your Lemma 1.1, see Lemma 4.4 in Ben-Eliezer, Ido; Krivelevich, Michael; Sudakov, Benny, The size Ramsey number of a directed path, J. Comb. Theory, Ser. B 102, No. 3, 743-755 (2012). ZBL124 …
Louis D's user avatar
  • 1,701