The graph complement of a graph hole. Graph antiholes are called even if they have an even number of vertices and odd if they have an odd number of vertices (Chvátal). No odd antihole is a perfect graph (since the clique number of an antihole with vertices is and its chromatic number is ).

# Graph Antihole

## See also

Berge Graph, Chordless Cycle, Graph Cycle, Graph Hole, Strong Perfect Graph Theorem## Explore with Wolfram|Alpha

## References

Chvátal, V. "The Strong Perfect Graph Theorem." http://www.cs.concordia.ca/~chvatal/perfect/spgt.html.## Referenced on Wolfram|Alpha

Graph Antihole## Cite this as:

Weisstein, Eric W. "Graph Antihole." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/GraphAntihole.html