Directed Graphclass: quasi-adjoint

Definition:

Let $N^+(x)$ be the out-neighbourhood of $x$.
A directed graph $G$ is a quasi-adjoint iff for any two vertices $x,y$ of $G$: If $N^+(x) \cap N^+(y) \neq\emptyset$ then $N^+(x) \subseteq N^+(y)$ or $N^+(y) \subseteq N^+(x)$, that is, the out-neighborhoods are nested.

References

[1632]
J. Blazewicz, M. Kasprzak, B. Leroy-Beaulieu, D. de Werra
Finding Hamiltonian circuits in quasi-adjoint graphs
Discrete Appl. Math. 156 2573-2580 (2008)

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Inclusions

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Map

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Maximal subclasses

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Parameters

Problems

Problems in italics have no summary page and are only listed when ISGCI contains a result for the current class.

Parameter decomposition

Unweighted problems

Graph isomorphism
[?]
Input: Graphs G and H in this class
Output: True iff G and H are isomorphic.
Unknown to ISGCI [+]Details
Hamiltonian cycle
[?]
Input: A graph G in this class.
Output: True iff G has a simple cycle that goes through every vertex of the graph.
Polynomial [+]Details
Hamiltonian path
[?]
Input: A graph G in this class.
Output: True iff G has a simple path that goes through every vertex of the graph.
Unknown to ISGCI [+]Details
Recognition
[?]
Input: A graph G.
Output: True iff G is in this graph class.
Polynomial [+]Details

Weighted problems