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Linear amortized time enumeration algorithms for compatible Euler trails in edge-colored graphs.
- Source :
- Journal of Combinatorial Optimization; Mar2023, Vol. 45 Issue 2, p1-20, 20p
- Publication Year :
- 2023
-
Abstract
- A compatible Euler trail (tour) in an edge-colored graph is an Euler trail (tour) in which each two edges traversed consecutively along the Euler trail (tour) have distinct colors. In this paper, we show that the problem of counting compatible Euler trails in edge-colored graphs is # P-complete, and develop O(mN) time algorithms for enumerating compatible Euler trails (tours) in edge-colored graphs with m edges and N compatible Euler trails (tours). It is worth mentioning that our algorithms can run in O(N) time when there is no vertex v with degree 4 and maximum monochromatic degree 2. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 13826905
- Volume :
- 45
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Journal of Combinatorial Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 162248416
- Full Text :
- https://doi.org/10.1007/s10878-023-01005-w