25 citations · 59 across the 14 of their papers we have counts for
18 papers
Tight paths in fully directed hypergraphs
Richard C. Devine, Kevin G. Milans
It is well-known that every tournament has a spanning path. We consider hypergraph analogues. In an \emph{-uniform fully directed hypergraph}, or \emph{-digraph}, every edge…
Longest Path and Cycle Transversals in Chordal Graphs
James A. Long, Kevin G. Milans, Michael C. Wigal
We show that if is a -vertex connected chordal graph, then it admits a longest path transversal of size . Under the stronger assumption of 2-connectivity, we sh…
Non-empty intersection of longest paths in -free graphs
James A. Long, Kevin G. Milans, Andrea Munaro
We make progress toward a characterization of the graphs such that every connected -free graph has a longest path transversal of size . In particular, we show that the gr…
Turán Numbers of Ordered Tight Hyperpaths
John P. Bright, Kevin G. Milans, Jackson Porter
An ordered hypergraph is a hypergraph whose vertex set is linearly ordered. We find the Turán numbers for the -uniform -vertex tight path (with vertice…
Sublinear Longest Path Transversals
James A. Long, Kevin G. Milans, Andrea Munaro
We show that connected graphs admit sublinear longest path transversals. This improves an earlier result of Rautenbach and Sereni and is related to the fifty-year-old question of w…
A Dichotomy Theorem for First-Fit Chain Partitions
Kevin G. Milans, Michael C. Wigal
First-Fit is a greedy algorithm for partitioning the elements of a poset into chains. Let be the maximum number of chains that First-Fit uses on a -free poset…