Discrrete mathematics for computer science DAG warmup

DAG Warm-Up Problem McNally and fellow guard Brandyn Curry, who combined for 26 second-half points, came up big for Harvard throughout the final frame After going scoreless in the first half, Curry scored 12 straight points for the Crimson off four three-pointers during a stretch of 3:27, turning a one-point deficit into a seven-point Harvard lead Indegree and outdegree of a vertex in a digraph • • Vertex v has outdegree Vertex has indegree v • • Lemma Any finite DAG has at least one node of indegree Proof In-class exercise Tournament Graph • A digraph is a tournament graph iff every pair of distinct nodes is connected by an edge in exactly one direction • Theorem: A tournament graph determines a unique ranking iff it is a DAG H P H Y D Y P D Tournament Graphs and Rankings • Theorem: A tournament graph determines a unique ranking iff it is a DAG • What does this mean? Tournament Graphs and Rankings • • • Theorem: A tournament graph determines a unique ranking iff it is a DAG What does this mean? That there is a unique sequence of the nodes, v1, …, vn, such that V = {v1, … vn} and for any i and j, i