Results 21 to 30 of about 4,527 (99)
TILING DIRECTED GRAPHS WITH TOURNAMENTS [PDF]
Forum of Mathematics, Sigma, 2016 The Hajnal–Szemerédi theorem states that for any positive integer $r$ and any multiple $n$ of $r$ , if $G$ is a graph on $n$ vertices and $\unicode[STIX]{x1D6FF}(G)\geqslant (1-1/r)n$ , then $G$ can be partitioned into $n/r$ vertex-disjoint copies of the
A. Czygrinow +3 more
semanticscholar +1 more source
Decomposing tournaments into paths
Proceedings of the London Mathematical Society, Volume 121, Issue 2, Page 426-461, August 2020., 2020 Abstract We consider a generalisation of Kelly's conjecture which is due to Alspach, Mason, and Pullman from 1976. Kelly's conjecture states that every regular tournament has an edge decomposition into Hamilton cycles, and this was proved by Kühn and Osthus for large tournaments. The conjecture of Alspach, Mason, and Pullman asks for the minimum number
Allan Lo +3 more
wiley +1 more source
Vertex‐disjoint properly edge‐colored cycles in edge‐colored complete graphs
Journal of Graph Theory, Volume 94, Issue 3, Page 476-493, July 2020., 2020 Abstract It is conjectured that every edge‐colored complete graph G on n vertices satisfying Δmon(G)≤n−3k+1 contains k vertex‐disjoint properly edge‐colored cycles. We confirm this conjecture for k=2, prove several additional weaker results for general k, and we establish structural properties of possible minimum counterexamples to the conjecture.
Ruonan Li, Hajo Broersma, Shenggui Zhang
wiley +1 more source
Hitting minors, subdivisions, and immersions in tournaments
, 2018 The Erd\H{o}s-P\'osa property relates parameters of covering and packing of combinatorial structures and has been mostly studied in the setting of undirected graphs.
Raymond, Jean-Florent
core +1 more source
Hamilton decompositions of regular tournaments [PDF]
, 2009 We show that every sufficiently large regular tournament can almost completely be decomposed into edge-disjoint Hamilton cycles. More precisely, for each \eta>0 every regular tournament G of sufficiently large order n contains at least (1/2-\eta)n edge ...
Kühn, Daniela +2 more
core +5 more sources
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 +4 more sources
Oriented coloring on recursively defined digraphs
, 2019 Coloring is one of the most famous problems in graph theory. The coloring problem on undirected graphs has been well studied, whereas there are very few results for coloring problems on directed graphs. An oriented k-coloring of an oriented graph G=(V,A)
Gurski, Frank +2 more
core +1 more source
, 2018 A digraph such that every proper induced subdigraph has a kernel is said to be \emph{kernel perfect} (KP for short) (\emph{critical kernel imperfect} (CKI for short) resp.) if the digraph has a kernel (does not have a kernel resp.).
Galeana-Sánchez, H., Olsen, M.
core +1 more source
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