Hostname: page-component-5b777bbd6c-7mr9c Total loading time: 0 Render date: 2025-06-22T05:06:57.762Z Has data issue: false hasContentIssue false
  • English
  • Français

Path Decompositions of Kneser and Generalized Kneser Graphs

Published online by Cambridge University Press:  20 November 2018

C. A. Rodger  and
Thomas Richard Whitt III
C. A. Rodger
Affiliation:
Department of Mathematics and Statistics, Auburn University, AL USA 36849-5310 e-mail: rodgec1@auburn.edutrw0003@auburn.edu
Thomas Richard Whitt III
Affiliation:
Department of Mathematics and Statistics, Auburn University, AL USA 36849-5310 e-mail: rodgec1@auburn.edutrw0003@auburn.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Necessary and sufficient conditions are given for the existence of a graph decomposition of the Kneser Graph $K{{G}_{n,2}}$ and of the Generalized Kneser Graph $GK{{G}_{n,3,1}}$ into paths of length three.

Keywords

05C5105C70Kneser graphgeneralized Kneser graphpath decompositiongraph decomposition
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 3 , 01 September 2015 , pp. 610 - 619
Copyright
Copyright © Canadian Mathematical Society 2015

References

[1] Alspach, B. and Gavlas, H., Cycle decompositions ofKn and Kn - I. J. Combin. Theory Ser. B 81(2001), 77–99. http://dx.doi.Org/10.1 OO6/jctb.2OOO.1 996 Google Scholar
[2] Bahmanian, A. and Rodger, C. A., Multiply Balanced Edge Colorings ofMultigraphs. J. Graph Theory, to appear.http://dx.doi.Org/10.1 OO2/jgt.2O617 Google Scholar
[3] Bârâny, I., A short proof of Kneser's conjecture. J. Combin. Theory Ser. A 25(1978), 325–326. http://dx.doi.Org/10.1016/0097-3165(78)90023-7 Google Scholar
[4] Chen, Y., Kneser graphs are Hamiltonian for n > 3k. J. Combin. Theory Ser. B 80(2000), 69–79. http://dx.doi.Org/10.1 OO6/jctb.2OOO.1 969 +3k.+J.+Combin.+Theory+Ser.+B+80(2000),+69–79.+http://dx.doi.Org/10.1+OO6/jctb.2OOO.1+969>Google Scholar
[5] Fu, H. L. and Rodger, C. A., Group divisible designs with two associate classes: n = 2 or m = 2. J. Combin. Theory Ser.A 83(1998), 94–117. http://dx.doi.Org/10.1006/jcta.1998.2868 Google Scholar
[6] Fu, H. L. and Rodger, C. A., 4-cycle group divisible designs with two associate classes. Combin. Probab.Comput. 10(2001), 317–343.Google Scholar
[7] Greene, J. E., A new short proof of Kneser's conjecture. Amer. Math. Monthly 109(2002), 918–920. http://dx.doi.Org/10.2307/3072460 Google Scholar
[8] Hoffman, D. G., Lindner, C. C., and Rodger, C. A., On the construction of odd cycle systems. J. Graph Theory 13(1989), 417–426. http://dx.doi.Org/10.1 OO2/jgt.3190130405 Google Scholar
[9] Kneser, M., Aufgabe 360. Jahresbericht der Deutschen Mathematiker-Vereinigung, 2.Abteilung 58(1955), 27.Google Scholar
[10] Lovâsz, L., Kneser's conjecture, chromatic number, and homotopy. J. Combin. Theory Ser. A 25(1978), 319–324. http://dx.doi.Org/10.1016/0097-3165(78)90022-5 Google Scholar
[11] Matousek, J., A combinatorial proof of Kneser's conjecture. Combinatorica 24(2004), 163–170. http://dx.doi.Org/10.1007/s00493-004-0011-1 Google Scholar
[12] Šajna, Mateja, On decomposing Kn -1 into cycles of a fixed odd length. In: Algebraic and topological methods in graph theory (Lake Bled, 1999). Discrete Math. 244(2002), 435–444. http://dx.doi.Org/10.101 6/S0012-365X(O1 )00099-1 Google Scholar
[13] Shields, Ian and Savage, Carla D., A note on Hamilton cycles in Kneser graphs. Bull. Inst. Combin. Appl. 40(2004), 13–22.Google Scholar
[14] Tarsi, Michael, Decomposition of a complete multigraph into simple paths: nonbalanced handcuffed designs. J. Combin. Theory Ser. A 34(1983), 60–70. http://dx.doi.org/!0.1016/0097-3165(83)90040-7 Google Scholar