Graphclass: even-cycle-free

Confusion danger: This class is sometimes called even-hole-free .

References

[1275]
Conforti, Michele; Cornuéjols, Gérard; Kapoor, Ajai; Vuskovic, Kristina
Even-hole-free graphs. I: Decomposition theorem
J. Graph Theory 39, No.1, 6-49 (2002)
[1276]
Conforti, Michele; Cornuéjols, Gérard; Kapoor, Ajai; Vuskovic, Kristina
Even-hole-free graphs. II: Recognition algorithm
J. Graph Theory 40, No.4, 238-266 (2002)

;

[1277]
M. Chudnovsky, K-i. Kawarabayashi, P. Seymour
Detecting even holes
J. Graph Theory 48, No.2, 85--111 (2005)
[1662]
M.V.G. da Silva, K. Vuskovic
Decomposition of even-hole-free graphs with star cutsets and 2-joins
J. of Combin. Th. (B) 103 No.1 144-183 (2013)
[1674]
H.-C. Chang, H.-I. Lu
A faster algorithm to recognize even-hole-free graphs
Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'12), 1286-1297, (2012)

Complement classes

Forbidden subgraphs

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Inclusions

The map shows the inclusions between the current class and a fixed set of landmark classes. Minimal/maximal is with respect to the contents of ISGCI. Only references for direct inclusions are given. Where no reference is given, check equivalent classes or use the Java application. To check relations other than inclusion (e.g. disjointness) use the Java application, as well.

Map

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Minimal superclasses

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Maximal subclasses

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Problems

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

3-Colourability
[?]
Input: A graph G in this class.
Output: True iff each vertex of G can be assigned one colour out of 3 such that whenever two vertices are adjacent, they have different colours.
Unknown to ISGCI [+]Details
Clique
[?]
Input: A graph G in this class and an integer k.
Output: True iff G contains a set S of pairwise adjacent vertices, with |S| >= k.
Polynomial [+]Details
Clique cover
[?]
Input: A graph G in this class and an integer k.
Output: True iff the vertices of G can be partitioned into k sets Si, such that whenever two vertices are in the same set Si, they are adjacent.
Unknown to ISGCI [+]Details
Cliquewidth
[?]
Whether the cliquewidth of the graphs in this class is bounded by a constant k .
The cliquewidth of a graph is the number of different labels that is needed to construct the graph using the following operations:
  • creation of a vertex with label i,
  • disjoint union,
  • renaming labels i to label j,
  • connecting all vertices with label i to all vertices with label j.
Unbounded [+]Details
Cliquewidth expression
[?]
Input: A graph G in this class.
Output: An expression that constructs G according to the rules for cliquewidth, using only a constant number of labels.
Undefined if this class has unbounded cliquewidth.
Unbounded or NP-complete [+]Details
Colourability
[?]
Input: A graph G in this class and an integer k.
Output: True iff each vertex of G can be assigned one colour out of k such that whenever two vertices are adjacent, they have different colours.
Unknown to ISGCI [+]Details
Cutwidth
[?]
Input: A graph G in this class and an integer k.
Output: True iff the cutwidth of G is at most k (see bounded cutwidth).
NP-complete [+]Details
Domination
[?]
Input: A graph G in this class and an integer k.
Output: True iff G contains a set S of vertices, with |S| <= k, such that every vertex in G is either in S or adjacent to a vertex in S.
NP-complete [+]Details
Feedback vertex set
[?]
Input: A graph G in this class and an integer k.
Output: True iff G contains a set S of vertices, with |S| <= k, such that every cycle in G contains a vertex from S.
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.
NP-complete [+]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.
NP-complete [+]Details
Independent set
[?]
Input: A graph G in this class and an integer k.
Output: True iff G contains a set S of pairwise non-adjacent vertices, such that |S| >= k.
Unknown to ISGCI [+]Details
Maximum cut
[?]
(decision variant)
Input: A graph G in this class and an integer k.
Output: True iff the vertices of G can be partitioned into two sets A,B such that there are at least k edges in G with one endpoint in A and the other endpoint in B.
NP-complete [+]Details
Recognition
[?]
Input: A graph G.
Output: True iff G is in this graph class.
Polynomial [+]Details
Treewidth
[?]
Input: A graph G in this class and an integer k.
Output: True iff the treewidth of G is at most k (see bounded treewidth).
Unknown to ISGCI [+]Details
Weighted clique
[?]
Input: A graph G in this class with weight function on the vertices and a real k.
Output: True iff G contains a set S of pairwise adjacent vertices, such that the sum of the weights of the vertices in S is at least k.
Polynomial [+]Details
Weighted feedback vertex set
[?]
Input: A graph G in this class with weight function on the vertices and a real k.
Output: True iff G contains a set S of vertices, such that the sum of the weights of the vertices in S is at most k and every cycle in G contains a vertex from S.
Unknown to ISGCI [+]Details
Weighted independent set
[?]
Input: A graph G in this class with weight function on the vertices and a real k.
Output: True iff G contains a set S of pairwise non-adjacent vertices, such that the sum of the weights of the vertices in S is at least k.
Unknown to ISGCI [+]Details
Weighted maximum cut
[?]
(decision variant)
Input: A graph G in this class with weight function on the edges and a real k.
Output: True iff the vertices of G can be partitioned into two sets A,B such that the sum of weights of the edges in G with one endpoint in A and the other endpoint in B is at least k.
NP-complete [+]Details