Results 21 to 30 of about 1,242,256 (73)
Strong arc decompositions of split digraphs
Journal of Graph Theory, Volume 108, Issue 1, Page 5-26, January 2025.Abstract A strong arc decomposition of a digraph D = ( V , A ) is a partition of its arc set A into two sets A 1 , A 2 such that the digraph D i = ( V , A i ) is strong for i = 1 , 2. Bang‐Jensen and Yeo conjectured that there is some K such that every K‐arc‐strong digraph has a strong arc decomposition. They also proved that with one exception on four
Jørgen Bang‐Jensen, Yun Wang
wiley +1 more source
Generalized tournaments and efficient orientations of graphs
, 2021 This thesis is concerned with both theoretical structural results whose possible applications are yet to be determined and algorithmic solutions to mathematical models inspired by real-world problems.
Surmacs, Michel
core
Seymour's second neighbourhood conjecture: random graphs and reductions
Random Structures &Algorithms, Volume 66, Issue 1, January 2025.Abstract A longstanding conjecture of Seymour states that in every oriented graph there is a vertex whose second outneighbourhood is at least as large as its outneighbourhood. In this short note we show that, for any fixed p∈[0,1/2)$$ p\in \left[0,1/2\right) $$, a.a.s.
Alberto Espuny Díaz +3 more
wiley +1 more source
Immersions of Directed Graphs in Tournaments
Random Structures &Algorithms, Volume 66, Issue 1, January 2025.ABSTRACT Recently, Draganić, Munhá Correia, Sudakov and Yuster (2022) showed that every tournament on (2+o(1))k2$$ \left(2+o(1)\right){k}^2 $$ vertices contains a 1‐subdivision of a transitive tournament on k$$ k $$ vertices, which is tight up to a constant factor. We prove a counterpart of their result for immersions.
António Girão, Robert Hancock
wiley +1 more source
Classes of intersection digraphs with good algorithmic properties
Journal of Graph Theory, Volume 106, Issue 1, Page 110-148, May 2024.Abstract While intersection graphs play a central role in the algorithmic analysis of hard problems on undirected graphs, the role of intersection digraphs in algorithms is much less understood. We present several contributions towards a better understanding of the algorithmic treatment of intersection digraphs.
Lars Jaffke +2 more
wiley +1 more source
Counting orientations of random graphs with no directed k‐cycles
Random Structures &Algorithms, Volume 64, Issue 3, Page 676-691, May 2024.Abstract For every k⩾3$$ k\geqslant 3 $$, we determine the order of growth, up to polylogarithmic factors, of the number of orientations of the binomial random graph containing no directed cycle of length k$$ k $$. This solves a conjecture of Kohayakawa, Morris and the last two authors.
Marcelo Campos +2 more
wiley +1 more source
, 1993 In this paper we introduce a generalization of digraphs that are locally tournaments (and hence of tournaments). This is the class of in-tournament digraphs-the set of predecessors of every vertex induces a tournament.
Bangjensen, J., Prisner, E., Huang, J.
core +1 more source
Hardness of subgraph and supergraph problems in c-tournaments [PDF]
, 2011 Problems like the directed feedback vertex set problem have much better algorithms in tournaments when compared to general graphs. This motivates us to study a natural generalization of tournaments, named c-tournaments, and see if the structural ...
Kanthi Kiran, S. +3 more
core +1 more source
On Seymour's and Sullivan's second neighbourhood conjectures
Journal of Graph Theory, Volume 105, Issue 3, Page 413-426, March 2024.Abstract For a vertex x $x$ of a digraph, d + ( x ) ${d}^{+}(x)$ (d − ( x ) ${d}^{-}(x)$, respectively) is the number of vertices at distance 1 from (to, respectively) x $x$ and d + + ( x ) ${d}^{++}(x)$ is the number of vertices at distance 2 from x $x$.
Jiangdong Ai +5 more
wiley +1 more source
07281 Open Problems – Structure Theory and FPT Algorithmcs for Graphs, Digraphs and Hypergraphs
, 2007 The following is a list of the problems presented on Monday, July 9, 2007 at the open-problem session of the Seminar on Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs, held at Schloss Dagstuhl in Wadern ...
Stege, Ulrike +3 more
core +1 more source