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On Colorful Edge Triples in Edge-Colored Complete Graphs

Gábor Simonyi
2020 Graphs and Combinatorics  
Investigating related Ramsey-type problems we also show that the Shannon (OR-)capacity of the Grötzsch graph is strictly larger than that of the cycle of length 5.  ...  one completely multicolored version of F.  ...  Note that M 3 is just C 5 and M 4 is the graph also called Grötzsch graph.  ... 
doi:10.1007/s00373-020-02214-4 fatcat:tifalwbz5beofblin5zakv54ba

Clique Colourings of Geometric Graphs

Colin McDiarmid, Dieter Mitsche, Pawel Prałat
2018 Electronic Journal of Combinatorics  
We investigate the clique chromatic number of such graphs.We first show that the clique chromatic number is at most 9 for any geometric graph in the plane, and briefly consider geometric graphs in higher  ...  The least number of colours in such a colouring is the clique chromatic number.  ...  Acknowledgements Thanks to Mike Saks, Lena Yuditsky and Shira Zerbib for helpful discussions, and thanks to an anonymous reviewer whose comments much improved the paper.  ... 
doi:10.37236/7159 fatcat:lpar4ch7azboljpdigaup7wrky

Clique colourings of geometric graphs [article]

Colin McDiarmid, Dieter Mitsche, Pawel Pralat
2018 arXiv   pre-print
The least number of colours in such a colouring is the clique chromatic number. Given n points x_1, ...,x_n in the plane, and a threshold r>0, the corresponding geometric graph has vertex set {v_1,...  ...  ,v_n}, and distinct v_i and v_j are adjacent when the Euclidean distance between x_i and x_j is at most r. We investigate the clique chromatic number of such graphs.  ...  Acknowledgements Thanks to Mike Saks, Lena Yuditsky and Shira Zerbib for helpful discussions, and thanks to an anonymous reviewer whose comments much improved the paper.  ... 
arXiv:1701.02693v2 fatcat:ajbg2da26vhs7lw2tgh2nm5ym4

Continuous Combinatorics of Abelian Group Actions [article]

Su Gao, Steve Jackson, Edward Krohne, Brandon Seward
2018 arXiv   pre-print
For example, we show that there is no continuous 3-coloring of the Cayley graph on F(2^Z^2), the free part of the shift action of Z^2 on 2^Z^2.  ...  With earlier work of the authors this computes the continuous chromatic number of F(2^Z^2) to be exactly 4.  ...  The Grötzsch Graph.  ... 
arXiv:1803.03872v1 fatcat:eugnyleahzgw7nlvy2da37tl5y

On Cylindrical Graph Construction and its Applications

Amir Daneshgar, Mohsen Hejrati, Meysam Madani
2016 unpublished
To show the applicability of the main duality we introduce generalized Grötzsch, generalized Petersen-like and Coxeter-like graphs and we prove some coloring properties of these graphs.  ...  In this article we introduce the cylindrical construction, as an edge-replacement procedure admitting twists on both ends of the hyperedges, generalizing the concepts of lifts and Pultr templates at the  ...  Acknowledgments The authors wish to thank an anonymous referee for her/his invaluable comments for improvement.  ... 
fatcat:h3yqi5vbmrfdllsed3svxd3od4