Gallai graphs and anti-Gallai graphs

@article{Le1996GallaiGA,
  title={Gallai graphs and anti-Gallai graphs},
  author={Van Bang Le},
  journal={Discrete Mathematics},
  year={1996},
  volume={159},
  pages={179-189}
}
The Gallai graph and the anti-Gallai graph of a graph G have the edges of G as their vertices. Two edges of G are adjacent in the Gallai graph of G if they are incident but do not span a triangle in G; they are adjacent in the anti-Gallai graph of G if they span a triangle in G. In this paper we show: The Four Color Theorem can be equivalently stated in terms of anti-Gallai graphs; the problems of determining the clique number, and the chromatic number of a Gallai graph are NP-complete… CONTINUE READING

From This Paper

Topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 13 extracted citations

Clique irreducibility of some iterative classes of graphs

Discussiones Mathematicae Graph Theory • 2008
View 4 Excerpts
Highly Influenced

Frontiers in Algorithmics and Algorithmic Aspects in Information and Management

Lecture Notes in Computer Science • 2013
View 6 Excerpts
Highly Influenced

References

Publications referenced by this paper.
Showing 1-10 of 17 references

Two classes of perfect graphs

J. Comb. Theory, Ser. B • 1991
View 4 Excerpts
Highly Influenced

On iterated triangular line graphs

E. B. Jarett
17th Conf. on Graph Theory, Combinatorics, Algorithms and Applications, Kalamazoo • 1992
View 3 Excerpts
Highly Influenced

Duality and perfection for edges in cliques

J. Comb. Theory, Ser. B • 1984
View 3 Excerpts
Highly Influenced

Graph Dynamics

E. Pilsner
Pitman Research Notes in Mathematics Series 338 • 1995
View 3 Excerpts

Iteratedk-line graphs

Graphs and Combinatorics • 1994
View 1 Excerpt

Mortality of iterated Gallai graphs

V. B. Le
Periodica Math. Hung. 27 • 1993
View 1 Excerpt

Perfect k-line graphs and k-total graphs

Journal of Graph Theory • 1993
View 1 Excerpt

Facet graphs of pure simplial complexes and related concepts

V. B. Le, E. Prisner
Preprint, Universit/it Hamburg • 1992
View 1 Excerpt

Recognizing claw-free perfect graphs

J. Comb. Theory, Ser. B • 1988
View 1 Excerpt

Similar Papers

Loading similar papers…