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-kernel (4) 4
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Journal of Graph Theory, ISSN 0364-9024, 06/2017, Volume 85, Issue 2, pp. 545 - 567
The k‐linkage problem is as follows: given a digraph D=(V,A) and a collection of k terminal pairs (s1,t1),…,(sk,tk) such that all these vertices are distinct;... 
polynomial algorithm | disjoint paths | k‐linkage problem | quasi‐transitive digraph | (round‐)decomposable digraphs | locally semicomplete digraph | (round-)decomposable digraphs | k-linkage problem | quasi-transitive digraph | MATHEMATICS | QUASI-TRANSITIVE DIGRAPHS | TOURNAMENTS | LOCALLY SEMICOMPLETE DIGRAPHS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 11/2013, Volume 313, Issue 22, pp. 2582 - 2591
Let D=(V(D),A(D)) be a digraph and k≥2 an integer. We say that D is k-quasi-transitive if for every directed path (v0,v1,…,vk) in D we have (v0,vk)∈A(D) or... 
Quasi-transitive digraph | Digraph | [formula omitted]-quasi-transitive digraph | [formula omitted]-king | Digraph k-king | k-quasi-transitive digraph | MATHEMATICS | 4-KINGS | 3-KINGS | k-king | KINGS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 08/2016, Volume 339, Issue 8, pp. 2094 - 2099
Let D=(V(D),A(D)) be a digraph and k be an integer with k≥2. A digraph D is k-quasi-transitive, if for any path x0x1…xk of length k, x0 and xk are adjacent. In... 
[formula omitted]-quasi-transitive digraph | Hamiltonian path | Quasi-transitive digraph | k-quasi-transitive digraph | MATHEMATICS | NUMBER | KINGS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 01/2015, Volume 338, Issue 1, pp. 114 - 121
Let D=(V(D),A(D)) be a digraph and k≥2 be an integer. A vertex x is a k-king of D, if for every y∈V(D), there is an (x,y)-path of length at most k. A subset N... 
[formula omitted]-kernel | Quasi-transitive digraph | [formula omitted]-quasi-transitive digraph | [formula omitted]-king | k-quasi-transitive digraph | k-king | k-kernel | MATHEMATICS | TOURNAMENTS | KERNELS
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 09/2014, Volume 77, Issue 2, pp. 89 - 110
We prove that the weak k‐linkage problem is polynomial for every fixed k for totally Φ‐decomposable digraphs, under appropriate hypothesis on Φ. We then apply... 
locally semicomplete digraph | cut‐width | decomposable digraph | quasi‐transitive digraph | arc‐disjoint paths | modular partition | weak linkages | cut-width | arc-disjoint paths | quasi-transitive digraph | MATHEMATICS
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 2083-5892, 05/2013, Volume 33, Issue 2, pp. 247 - 260
Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is transitive if for every three distinct vertices... 
4-transitive digraph | k-quasi-transitive digraph | k-transitive digraph | digraph | transitive digraph | quasi-transitive digraph | K-transitive digraph | Transitive digraph | Quasi-transitive digraph | Digraph | K-quasi-transitive digraph | MATHEMATICS | quasi-transitive digraph,4-transitive digraph
Journal Article
Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 11/2017, Volume 62, pp. 213 - 218
Let k be an integer, k≥2. A digraph D=(V,A) is k-quasi-transitive if for every pair of vertices u,v∈V, the existence of a directed path of length k from u to v... 
k-quasi-transitive digraph | traceability | quasi-transitive digraph | Hamiltonicity
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 07/2017, Volume 226, pp. 44 - 50
In 2014 D. Pálvölgyi and A. Gyárfás explored the minimum dominating set of a digraph with an arc partition into transitive digraphs. A. Gyárfás proposed the... 
Dominating sets | Quasi-transitive digraphs | Vertex partitions | MATHEMATICS, APPLIED
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 05/2015, Volume 79, Issue 1, pp. 55 - 62
Let D be a digraph with vertex set V(D) and arc set A(D). A vertex x is a k‐king of D, if for every y∈V(D), there is an (x,y)‐path of length at most k. A... 
quasitransitive digraph | k‐quasitransitive digraph | k‐king | k‐kernel | k-quasitransitive digraph | k-king | k-kernel | MATHEMATICS | QUASI-TRANSITIVE DIGRAPHS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 08/2012, Volume 312, Issue 16, pp. 2522 - 2530
Let D be a digraph, V(D) and A(D) will denote the sets of vertices and arcs of D, respectively. A subset N of V(D) is k-independent if for every pair of... 
[formula omitted]-kernel | Transitive digraph | Quasi-transitive digraph | Digraph | Kernel | (k, l) -kernel | k-kernel | MATHEMATICS | 3-KINGS | (k, l)-kernel | KINGS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 05/2020, Volume 372, p. 124964
A digraph D is supereulerian if D contains a spanning eulerian subdigraph. For any distinct four vertices c1, c2, c3, c4 of D, D is H1-quasi-transitive if... 
Arc-strong connectivity | Supereulerian digraph | Eulerian factor | Spanning closed ditrail | Independence number | 3-path-quasi-transitive digraph | MATHEMATICS, APPLIED
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 2083-5892, 05/2013, Volume 33, Issue 2, pp. 429 - 435
A digraph is 3-quasi-transitive (resp. 3-transitive), if for any path x0x1 x2x3 of length 3, x0 and x3 are adjacent (resp. x0 dominates x3). C´esar... 
graph orientation | 3-quasi-transitive digraph | 3-transitive digraph | Graph orientation | MATHEMATICS | QUASI-TRANSITIVE DIGRAPHS
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 5/2019, Volume 35, Issue 3, pp. 669 - 675
Kernel is an important topic in digraphs. A digraph such that every proper induced subdigraph has a kernel is said to be critical kernel imperfect (CKI, for... 
Arc-locally in-semicomplete digraph | 05C20 | Generalization of bipartite tournaments | CKI-digraph | Mathematics | Engineering Design | Combinatorics | 3-Anti-quasi-transitive digraph | 05C69 | Kernel | 3-Quasi-transitive digraph | MATHEMATICS | Kernels | Asymmetry | Graph theory
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 2083-5892, 05/2013, Volume 33, Issue 2, pp. 247 - 260
Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is transitive if for every three distinct vertices... 
4-transitive digraph | k-quasi-transitive digraph | digraph | k-transitive digraph | transitive digraph | quasi-transitive digraph
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 11/2014, Volume 34, Issue 4, pp. 651 - 671
A digraph D is k-transitive if the existence of a directed path (v0, v1, . . . , vk), of length k implies that (v0, vk) ∈ A(D). Clearly, a 2-transitive digraph... 
k-quasi-transitive digraph | k-transitive digraph | digraph | Laborde-Payan-Xuong Conjecture | transitive digraph | quasi-transitive digraph | Transitive digraph | Quasi-transitive digraph | Digraph | Laborde-Payan-Xuong conjecture | MATHEMATICS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2010, Volume 158, Issue 5, pp. 461 - 466
A digraph D is a union of quasi-transitive digraphs if its arcs can be partitioned into sets A 1 and A 2 such that the induced subdigraph D [ A i ] ( i = 1 , 2... 
Quasi-transitive chromatic class | Kernel by monochromatic paths | [formula omitted]-colored quasi-transitive digraphs | m-colored quasi-transitive digraphs | MATHEMATICS, APPLIED | TOURNAMENTS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2006, Volume 306, Issue 16, pp. 1969 - 1974
Let D be a digraph, V ( D ) and A ( D ) will denote the sets of vertices and arcs of D, respectively. A kernel N of D is an independent set of vertices such... 
Kernel-perfect digraph | Kernel | Quasi-transitive digraph | kernel-perfect digraph | MATHEMATICS | PERFECT | quasi-transitive digraph | kernel | GRAPHS
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 2083-5892, 02/2014, Volume 34, Issue 1, pp. 167 - 185
Let D be a digraph with the vertex set V (D) and the arc set A(D). A subset N of V (D) is k-independent if for every pair of vertices u, v ∈ N, we have d(u,... 
3-kernel | k-quasi-transitive digraph | multipartite tournament | cyclically 3-partite digraphs | kernel | NP-completeness | Multipartite tournament | Kernel | K-quasi-transitive digraph | Cyclically 3-partite digraphs | MATHEMATICS | QUASI-TRANSITIVE DIGRAPHS | KERNELS
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 08/2014, Volume 34, Issue 3, pp. 431 - 466
Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A (k, l)-kernel N of D is a k-independent (if u, v ∈ N, u 6=... 
kernel | k-kernel | infinite digraph | l)-kernel | Infinite digraph | K-kernel | Kernel | (k, l)-kernel | MATHEMATICS | NUMBER | QUASI-TRANSITIVE DIGRAPHS | KERNELS | GRAPHS
Journal Article
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