## 66 Citations

### Locally Semicomplete Digraphs and Generalizations

- MathematicsClasses of Directed Graphs
- 2018

This chapter surveys a number of important results, both structural and algorithmic, on locally semicomplete digraphs and illustrates various important proof-techniques.

### A Characterization of Locally Semicomplete CKI-digraphs

- MathematicsGraphs Comb.
- 2016

It is concluded that determinate whether a locally semicomplete digraph is a CKI-digraph or not, is polynomial.

### Linkages in locally semicomplete digraphs and quasi-transitive digraphs

- MathematicsDiscret. Math.
- 1999

### LOCALLY SEMICOMPLETE DIGRAPHS WITH A FACTOR COMPOSED OF k CYCLES

- Mathematics
- 2004

A digraph is locally semicomplete if for every vertex x, the set of in-neighbors as well as the set of out-neighbors of x induce semicomplete digraphs. Let D be a k-connected locally semicomplete…

### Arc-Disjoint Hamiltonian Cycles in Round Decomposable Locally Semicomplete Digraphs

- MathematicsDiscuss. Math. Graph Theory
- 2018

It is proved that every 3-strong round decomposable locally semicomplete digraph has two arc-disjoint Hamiltonian cycles, which implies that the conjecture holds for the round decomPOSable local tournaments.

### The complexity of digraph homomorphisms: local tournaments, injective homomorphisms and polymorphisms

- Mathematics
- 2008

In this thesis we examine the computational complexity of certain digraph homomorphism problems. A homomorphism between digraphs, denoted by f : G → H, is a mapping from the vertices of G to the…

### Decomposing locally semicomplete digraphs into strong spanning subdigraphs

- MathematicsJ. Comb. Theory, Ser. B
- 2012

### Chordality of locally semicomplete and weakly quasi-transitive digraphs

- MathematicsDiscret. Math.
- 2021

## References

SHOWING 1-10 OF 43 REFERENCES

### Locally semicomplete digraphs: A generalization of tournaments

- MathematicsJ. Graph Theory
- 1990

The class of underlying graphs of the locally semi-complete digraphs is precisely the class of proper circular-arc graphs (see [13], Theorem 3), and it is shown that many of the classic theorems for tournaments have natural analogues for locally semicompleteDigraphs.

### Local Tournaments and Proper Circular Arc Gaphs

- MathematicsSIGAL International Symposium on Algorithms
- 1990

It turns out that these chordal graphs that are orientable as local tournaments are precisely the graphs previously studied as proper circular arc graphs, i.e., that are proper circularArc graphs.

### Connectivity properties of locally semicomplete digraphs

- MathematicsJ. Graph Theory
- 1994

It is shown that every k-connected locally semicomplete digraph D with minimum outdegree at least 2k and minimum indegree at least 2k − 2 has at least m = max{2, k} vertices x1, x2, , xm such that D…

### Sucient conditions for a digraph to be Hamiltonian

- Mathematics
- 1996

We describe a new type of sufficient condition for a digraph to be Hamiltonian. Conditions of this type combine local structure of the digraph with conditions on the degrees of non-adjacent vertices.…

### Tournament-like oriented graphs

- Mathematics
- 1992

A local tournament is an oriented graph in which the inset as well as the outset of each vertex induces a tournament. Local tournaments possess many properties of tournaments and have interesting…

### Sufficient conditions for a digraph to be Hamiltonian

- MathematicsJ. Graph Theory
- 1996

A new type of sufficient condition for a digraph to be Hamiltonian is described, which combines local structure of the digraph with conditions on the degrees of non-adjacent vertices.

### On the Structure of Local Tournaments

- MathematicsJ. Comb. Theory, Ser. B
- 1995

A method to generate all local tournaments by performing some simple operations on some simple basic oriented graphs is described and a description of all local tournament with the same underlying proper circular are graph is obtained.