Results 21 to 30 of about 1,490 (70)
Journal of Graph Theory, Volume 110, Issue 1, Page 82-91, September 2025.ABSTRACT An inversion of a tournament T is obtained by reversing the direction of all edges with both endpoints in some set of vertices. Let inv k ( T ) be the minimum length of a sequence of inversions using sets of size at most k that result in the transitive tournament.
Raphael Yuster
wiley +1 more source
Edge‐arc‐disjoint paths in semicomplete mixed graphs
Journal of Graph Theory, Volume 108, Issue 4, Page 705-721, April 2025.Abstract The so‐called weak‐2‐linkage problem asks for a given digraph D=(V,A) $D=(V,A)$ and distinct vertices s1,s2,t1,t2 ${s}_{1},{s}_{2},{t}_{1},{t}_{2}$ of D $D$ whether D $D$ has arc‐disjoint paths P1,P2 ${P}_{1},{P}_{2}$ so that Pi ${P}_{i}$ is an (si,ti) $({s}_{i},{t}_{i})$‐path for i=1,2 $i=1,2$. This problem is NP‐complete for general digraphs
J. Bang‐Jensen, Y. Wang
wiley +1 more source
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
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
A sufficient condition for pre-Hamiltonian cycles in bipartite digraphs
, 2017 Let $D$ be a strongly connected balanced bipartite directed graph of order $2a\geq 10$ other than a directed cycle. Let $x,y$ be distinct vertices in $D$.
Darbinyan, Samvel Kh. +1 more
core +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
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
Vertices with the Second Neighborhood Property in Eulerian Digraphs
, 2014 The Second Neighborhood Conjecture states that every simple digraph has a vertex whose second out-neighborhood is at least as large as its first out-neighborhood, i.e. a vertex with the Second Neighborhood Property.
Dong-Lan Luo (608306) +8 more
core +3 more sources