Results 11 to 20 of about 1,500 (66)
Journal of the London Mathematical Society, Volume 108, Issue 5, Page 1852-1885, November 2023., 2023 Abstract A k$k$‐uniform hypergraph M$M$ is set‐homogeneous if it is countable (possibly finite) and whenever two finite induced subhypergraphs U,V$U,V$ are isomorphic there is g∈Aut(M)$g\in \mathop {\rm Aut}\nolimits (M)$ with Ug=V$U^g=V$; the hypergraph M$M$ is said to be homogeneous if in addition every isomorphism between finite induced ...
Amir Assari +2 more
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Complementary cycles of any length in regular bipartite tournaments
Journal of Graph Theory, Volume 103, Issue 2, Page 186-211, June 2023., 2023 Abstract Let D $D$ be a k $k$‐regular bipartite tournament on n $n$ vertices. We show that, for every p $p$ with 2≤p≤n∕2−2 $2\le p\le n\unicode{x02215}2-2$, D $D$ has a cycle C $C$ of length 2p $2p$ such that D\C $D\backslash C$ is Hamiltonian unless D $D$ is isomorphic to the special digraph F4k ${F}_{4k}$.
Stéphane Bessy, Jocelyn Thiebaut
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On coloring digraphs with forbidden induced subgraphs
Journal of Graph Theory, Volume 103, Issue 2, Page 323-339, June 2023., 2023 Abstract We prove a conjecture by Aboulker, Charbit, and Naserasr by showing that every oriented graph in which the out‐neighborhood of every vertex induces a transitive tournament can be partitioned into two acyclic induced subdigraphs. We prove multiple extensions of this result to larger classes of digraphs defined by a finite list of forbidden ...
Raphael Steiner
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Making a tournament k $k$‐strong
Journal of Graph Theory, Volume 103, Issue 1, Page 5-11, May 2023., 2023 Abstract A digraph is k ${\bf{k}}$‐strong if it has n ≥ k + 1 $n\ge k+1$ vertices and every induced subdigraph on at least n − k + 1 $n-k+1$ vertices is strongly connected. A tournament is a digraph with no pair of nonadjacent vertices. We prove that every tournament on n ≥ k + 1 $n\ge k+1$ vertices can be made k $k$‐strong by adding no more than k ...
Jørgen Bang‐Jensen +2 more
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Spanning eulerian subdigraphs in semicomplete digraphs
Journal of Graph Theory, Volume 102, Issue 3, Page 578-606, March 2023., 2023 Abstract A digraph is eulerian if it is connected and every vertex has its in‐degree equal to its out‐degree. Having a spanning eulerian subdigraph is thus a weakening of having a hamiltonian cycle. In this paper, we first characterize the pairs (D,a) $(D,a)$ of a semicomplete digraph D $D$ and an arc a $a$ such that D $D$ has a spanning eulerian ...
Jørgen Bang‐Jensen +2 more
wiley +1 more source
Path decompositions of tournaments
Proceedings of the London Mathematical Society, Volume 126, Issue 2, Page 429-517, February 2023., 2023 Abstract In 1976, Alspach, Mason, and Pullman conjectured that any tournament T$T$ of even order can be decomposed into exactly ex(T)$\operatorname{ex}(T)$ paths, where ex(T)≔12∑v∈V(T)|dT+(v)−dT−(v)|$\operatorname{ex}(T)\coloneqq \frac{1}{2}\sum _{v\in V(T)}|d_T^+(v)-d_T^-(v)|$. We prove this conjecture for all sufficiently large tournaments.
António Girão +4 more
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On Tight Tree‐Complete Hypergraph Ramsey Numbers
Journal of Graph Theory, EarlyView.ABSTRACT Chvátal showed that for any tree T $T$ with k $k$ edges, the Ramsey number R ( T , n ) = k ( n − 1 ) + 1 $R(T,n)=k(n-1)+1$. For r = 3 $r=3$ or 4, we show that, if T $T$ is an r $r$‐uniform nontrivial tight tree, then the hypergraph Ramsey number R ( T , n ) = Θ ( n r − 1 ) $R(T,n)={\rm{\Theta }}({n}^{r-1})$.
Jiaxi Nie
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Interdiction Models and Heuristics for Graph Propagation
Networks, EarlyView.ABSTRACT Given a graph G=(V,E)$$ G=\left(V,E\right) $$ and a set S⊂V$$ S\subset V $$ of activated/infected nodes, we consider the problem of determining the set of c$$ c $$ nodes that minimizes the network propagation on the subgraph that results from the removal of those c$$ c $$ nodes. To measure network propagation, we assume that a node i$$ i $$ is
Agostinho Agra, José Maria Samuco
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Properly Colored Cycles in Edge‐Colored Balanced Bipartite Graphs
Journal of Graph Theory, Volume 112, Issue 2, Page 37-53, June 2026.ABSTRACT Let G n , n c denote a (not necessarily properly) edge‐colored balanced bipartite graph on 2 n vertices, that is, in which every edge is assigned a color. A cycle C in G n , n c is called properly colored if any two consecutive edges of C have distinct colors.
Tingting Han +3 more
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Number of Subgraphs and Their Converses in Tournaments and New Digraph Polynomials
Journal of Graph Theory, Volume 110, Issue 2, Page 127-131, October 2025.ABSTRACT An oriented graph D is converse invariant if, for any tournament T, the number of copies of D in T is equal to that of its converse − D. El Sahili and Ghazo Hanna [J. Graph Theory 102 (2023), 684‐701] showed that any oriented graph D with maximum degree at most 2 is converse invariant. They proposed a question: Can we characterize all converse
Jiangdong Ai +4 more
wiley +1 more source