Proves a transversal version of Ghouila-Houri's theorem on directed Hamilton cycles in digraph collections, solving an open problem of Chakraborti et al.
Rota’s Basis Conjecture holds asymptotically
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The paper finds the threshold probability for random subgraphs of Dirac graphs to admit Hamilton cycle transversals and derives optimal counting and packing corollaries that generalize single-graph Hamilton cycle results.
Survey compiling sufficient conditions for transversal m-edge structures in graph systems that extend classical extremal graph theory results, plus conjectures.
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Transversal Hamilton cycles in digraph collections
Proves a transversal version of Ghouila-Houri's theorem on directed Hamilton cycles in digraph collections, solving an open problem of Chakraborti et al.
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Robust Hamiltonicity in families of Dirac graphs
The paper finds the threshold probability for random subgraphs of Dirac graphs to admit Hamilton cycle transversals and derives optimal counting and packing corollaries that generalize single-graph Hamilton cycle results.
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Transversal Structures in Graph Systems: A Survey
Survey compiling sufficient conditions for transversal m-edge structures in graph systems that extend classical extremal graph theory results, plus conjectures.