A decomposition of gallai multigraphs

• Autorzy: Alexander Halperin , Colton Magnant , Kyle Pula
• Języki publikacji: EN

Abstrakty

EN

An edge-colored cycle is rainbow if its edges are colored with distinct colors. A Gallai (multi)graph is a simple, complete, edge-colored (multi)graph lacking rainbow triangles. As has been previously shown for Gallai graphs, we show that Gallai multigraphs admit a simple iterative construction. We then use this structure to prove Ramsey-type results within Gallai colorings. Moreover, we show that Gallai multigraphs give rise to a surprising and highly structured decomposition into directed trees

Słowa kluczowe

EN

edge coloring; Gallai multigraph

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 2
• Strony: 331-352

Daty

wydano

2014-05-01

online

2014-04-12

Twórcy

autor

Alexander Halperin

• Department of Mathematics Lehigh University Bethlehem, PA 18015, U.S.A.

autor

Colton Magnant

• Department of Mathematical Sciences Georgia Southern University Statesboro, GA 30460, U.S.A

autor

Kyle Pula

• Department of Mathematics University of Denver Denver, CO 80208, U.S.A

Bibliografia

• [1] B. Alexeev, On lengths of rainbow cycles, Electron. J. Combin. 13(1) (2006) #105
• [2] R.N. Ball, A. Pultr and P. Vojtěchovský, Colored graphs without colorful cycles, Combinatorica 27 (2007) 407-427. doi:10.1007/s00493-007-2224-6[WoS][Crossref]
• [3] A. Diwan and D. Mubayi, Turán’s theorem with colors, preprint, 2007.
• [4] R.J. Faudree, R. Gould, M. Jacobson and C. Magnant, Ramsey numbers in rainbow triangle free colorings, Australas. J. Combin. 46 (2010) 269-284.
• [5] A. Frieze and M. Krivelevich, On rainbow trees and cycles, Electron. J. Combin. 15 (2008) #59.
• [6] S. Fujita and C. Magnant, Extensions of Gallai-Ramsey results, J. Graph Theory 70 (2012) 404-426. doi:10.1002/jgt.20622[Crossref]
• [7] S. Fujita and C. Magnant, Gallai-Ramsey numbers for cycles, Discrete Math. 311 (2011) 1247-1254. doi:10.1016/j.disc.2009.11.004[Crossref]
• [8] S. Fujita, C. Magnant and K. Ozeki, Rainbow generalizations of Ramsey theory: a survey, Graphs Combin. 26 (2010) 1-30. doi:10.1007/s00373-010-0891-3[Crossref][WoS]
• [9] S. Fujita, C. Magnant and K. Ozeki. Rainbow generalizations of Ramsey theory: a survey, (2011) updated. http://math.georgiasouthern.edu/∼cmagnant
• [10] T. Gallai, Transitiv orientierbare Graphen, Acta Math. Acad. Sci. Hungar. 18 (1967) 25-66. doi:10.1007/BF02020961[Crossref]
• [11] A. Gyárfás, G. Sárközy, A. Sebö and S. Selkow, Ramsey-type results for Gallai colorings, J. Graph Theory 64 (2010) 233-243.[WoS]
• [12] A. Gyárfás and G. Simonyi, Edge colorings of complete graphs without tricolored triangles, J. Graph Theory 46 (2004) 211-216. doi:10.1002/jgt.20001[Crossref]
• [13] P. Vojtěchovský, Periods in missing lengths of rainbow cycles, J. Graph Theory 61 (2009) 98-110. doi:10.1002/jgt.20371 [Crossref][WoS]

Identyfikatory

DOI

10.7151/dmgt.1740