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DTSTART:20260308T070000
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DTSTART;TZID=America/Toronto:20260810T140000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/masters-thes
 is-presentation-david-evangelista-backedge
SUMMARY:Master's Thesis Presentation - David Evangelista - Backedge Graphs 
 of\nTournaments: Algorithms and Complexity
CLASS:PUBLIC
DESCRIPTION:SPEAKER:\n David Evangelista\n\nSUPERVISOR(S):\n Joseph Cheriya
 n and Sophie Spirkl\n\nCOMMITTEE:\n Jane Gao\, Eric Blais\n\nLOCATION:\n M
 C 5417\n\nABSTRACT: \n\nA tournament $\\T=(V\,A)$ on $n$ vertices is an o
 rientation of the\ncomplete graph $K_n$. The backedge graph of $T$ with re
 spect to an\nordering of $V$ is the undirected graph on vertex set $V$ who
 se edge\nset corresponds to the arcs directed from a later vertex to an ea
 rlier\nvertex in the ordering. Backedge graphs provide concise\nrepresenta
 tions of the tournament. The algorithmic problem of\ndetermining whether a
  tournament admits a backedge graph in a given\nclass of undirected graphs
  varies in complexity\, and is often\nequivalent to computing parameters o
 f tournaments\, such as\ndegreewidth when the backedge graph has bounded 
 maximum degree\n\\cite{Davot et al.\, 2023}. We extend the notion of degre
 ewidth by\nintroducing directional degreewidth\, which separately bounds t
 he\nleft-degrees and right-degrees of vertices in addition to bounding the
 \ntotal degrees. We obtain an algorithm for verifying bounds on the\ndirec
 tional degreewidth of the tournament\, whose runtime is polynomial\ntime w
 hen the total degree is unbounded\, or fixed-parameter tractable\ntime wit
 h respect to the total degree bound otherwise. We also provide\na polynomi
 al-time algorithm for computing a $P_3$-free backedge graph\nof a tourname
 nt\, if it exists. Together with existing results\, the\nlatter result set
 tles the complexity of determining whether a\ntournament admits an $H$-fre
 e backedge graph when $H$ is any graph on\nthree vertices.
DTSTAMP:20260804T154614Z
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