Long rainbow cycles and Hamiltonian cycles using many colors in properly edge-colored complete graphs
- Award ID(s):
- 1800761
- PAR ID:
- 10106753
- Date Published:
- Journal Name:
- European Journal of Combinatorics
- Volume:
- 79
- Issue:
- C
- ISSN:
- 0195-6698
- Page Range / eLocation ID:
- 140 to 151
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We prove that every family of (not necessarily distinct) even cycles D_1,...,D_{1.2n-1} on some fixed n-vertex set has a rainbow even cycle (that is, a set of edges from distinct D_i’s, forming an even cycle). This resolves an open problem of Aharoni, Briggs, Holzman and Jiang. Moreover, the result is best possible for every positive integer n.more » « less
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