Linear amortized time enumeration algorithms for compatible Euler trails in edge-colored graphs

Yuhang Bai (), Zhiwei Guo (), Shenggui Zhang () and Yandong Bai ()
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Yuhang Bai: Northwestern Polytechnical University
Zhiwei Guo: Yan’an University
Shenggui Zhang: Northwestern Polytechnical University
Yandong Bai: Northwestern Polytechnical University

Journal of Combinatorial Optimization, 2023, vol. 45, issue 2, No 19, 20 pages

Abstract: 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.

Keywords: Edge-colored graph; Compatible Euler trail; Enumeration algorithm; Linear amortized time; 05C15; 05C30; 05C45; 05C85 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-023-01005-w

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