Stability of transversal Hamilton cycles and paths Article Swipe
Related Concepts
Transversal (combinatorics)
Stability (learning theory)
Mathematics
Computer science
Mathematical analysis
Machine learning
Y. Cheng
,
Katherine Staden
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2403.09913
· OA: W4392929887
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2403.09913
· OA: W4392929887
Given graphs $G_1,\ldots,G_s$ all on a common vertex set and a graph $H$ with $e(H) = s$, a copy of $H$ is \emph{transversal} or \emph{rainbow} if it contains one edge from each $G_i$. We establish a stability result for transversal Hamilton cycles: the minimum degree required to guarantee a transversal Hamilton cycle can be lowered as long as the graph collection $G_1,\ldots,G_n$ is far in edit distance from several extremal cases. We obtain an analogous result for Hamilton paths. The proof is a combination of our newly developed regularity-blow-up method for transversals, along with the absorption method.
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