Some articles about applications of Mixed Hypergraph Coloring in different areas:
In Ramsey type problems:
- 255. D. Slutzky, V. Voloshin. The Chromatic Spectrum of a Ramsey Mixed Hypergraph. Computer Science Journal of Moldova, vol. 24, no.2(71), 2016, pp. 213-233.
In distributed computing (in part related to cyber-security):
- Access Control Model for the Inference Attacks with Access Histories. Computer Software and Applications Conference (COMPSAC), 2017 IEEE 41st Annual. .
- Chuanyou Li; Michel Hurfin; Yun Wang; Lei Yu. Towards a Restrained Use of Non-Equivocation for Achieving Iterative Approximate Byzantine Consensus. 2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS)
- H. Zhang, L. Song, Z. Han. Radio Resource Allocation for Device-to-Device Underlay Communication Using Hypergraph Theory. IEEE Transactions on Wireless Communications (Volume:15, Issue: 7, 2016).
- S. Sen. New Systems and Algorithms for Scalable Fault Tolerance. PhD Thesis, Princeton University, 2013, 154 p.
- Alexander Jaffe, Thomas Moscibroda, Siddhartha Sen. On the price of equivocation in byzantine agreement. Proceeding PODC ’12 Proceedings of the 2012 ACM symposium on Principles of distributed computing Pages 309-318
- Alexander Jaffe, Thomas Moscibroda, Siddhartha Sen. On the Price of Equivocation in Byzantine Agreement. Microsoft Research, Microsoft Corporation 2012.
In WORM and similar/related graph coloring:
/brilliant examples showing that basic concepts of mixed hypergraph coloring provide a wealthy source of infinitely many beautiful problems in graph theory/
- Chandler, James D.; Desormeaux, Wyatt J.; Haynes, Teresa W.; Hedetniemi, Stephen T. Neighborhood-restricted [≤2]-achromatic colorings. Discrete Appl. Math. 207 (2016), 39–44.
- Honghai Xu. Generalized Colorings of Graphs. PhD Thesis. Clemson University, 2016
- J. Chandler. Neighborhood-Restricted Achromatic Colorings of Graphs. PhD Thesis. East Tennessee State University, 2016.
- Cs. Bujtas, Zs. Tuza. F-WORM colorings: Results for 2-connected graphs.
- Cs. Bujtas, Zs. Tuza. K3-WORM colorings of graphs: Lower chromatic number and gaps in the chromatic spectrum. Submitted.
- MR3308543 Goddard, Wayne; Wash, Kirsti; Xu, Honghai. WORM colorings forbidding cycles or cliques. Congr. Numer. 219 (2014), 161-173.
- MR3368990 Goddard, Wayne; Wash, Kirsti; Xu, Honghai. Worm colorings. Discuss. Math. Graph Theory 35 (2015), no. 3, 571–584
Special comment. After you pick a class of graphs and two subgraphs of interest for C- and D-edges, the following questions become very interesting immediately:
- conditions of uncolorability
- conditions of unique colorability
- values of the upper and lower chromatic numbers
- continuity of the chromatic spectrum
- perfection with respect to the upper chromatic number
- the values of entries in the chromatic spectrum
- chromatic polynomial (roots, coefficients)
- algorithmic aspects of finding all of the above
In general graph and hypergraph coloring theory:
- D. Kral. Mixed Hypergraphs and other coloring problems. Discrete Mathematics 307 (7-8) (2007), 923-938.
In general (range from molecular biology to philosophy):
- V.I. Voloshin. Coloring Mixed Hypergraphs: theory, algorithms and applications. AMS, Providence, 2002.
In coloring of Block Designs:
- 228. M. Gionfriddo, V. Voloshin. Bihypergraphs and G-Designs with Broken Chromatic Spectrum: Results and Problems. Applied Mathematical Sciences, Vol. 8, 2014, no. 74, 3673 – 3682.
- 205. J. Matthews. Maximal induced colorable subhypergraphs of all uncolorable BSTS(15)s. Computer Science Journal of Moldova, vol.19, no. 1(55), 2011, pp. 29- 37.
- 185. L. Milazzo, Zs. Tuza. Logarithmic upper bound for the upper chromatic number of $S(t,t+1,v)$ systems. Ars Combin. 92 (2009), 213–223.
- 143. M. Gionfriddo, L. Milazzo, A. Rosa, V. Voloshin. Bicoloring Steiner systems S(2,4,v). Discrete Mathematics, 283 (2004) 249-253.
- 123. L. Gionfriddo. P(3)-designs with gaps in the chromatic spectrum. Rendiconti Seminario Matematico Universita Messina 8 (2002), 49-58.
- 91. M. Buratti, M. Gionfriddo, L. Milazzo, V. Voloshin. Lower and upper chromatic numbers for BSTSs(2^h – 1). Comput. Sci. J. Moldova, Vol. 9, No 2, (2001), 259-272.
- 86. G. Lo Faro, L. Milazzo, A. Tripodi. On the Upper and Lower Chromatic Numbers of BSQSs(16). Electron. J. Combin. 8(1) (2001) R6.
- 83. G. Lo Faro, L. Milazzo, A. Tripodi. The first BSTS with different upper and lower chromatic numbers. Australas. J. Combin. 22 (2000), 123–133.
- 58. Ch. Colbourn, J. Dinitz and A. Rosa. Bicoloring Steiner Triple Systems. Electron. J. Combin. 6 (1999), R25.
- 57. Ch.J. Colbourn, A. Rosa. Triple Systems. Clarendon Press, Oxford, 1999 (section 18.6. Strict colorings and the upper chromatic number, p. 340-341).
- 44. L. Milazzo, Zs. Tuza. Strict Colourings for Classes of Steiner Triple Systems. Discrete Math., 182 (1998) 233-243.
- 171. P. Johnson, V. Voloshin. Geombinatorial Mixed Hypergraph Coloring Problems. Geombinatorics, Vol XVII (2), 2007, 57-67.