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Kevin Bacon, Paul Erd˝Os, William Mckinley The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory Ryan Martin [email protected] Mathematics Department Iowa State University Joint Work This talk is based on joint work with Tom Bohman, Carnegie Mellon University Alan Frieze, Carnegie Mellon University Michael Krivelevich, Tel Aviv University The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.1/64 Six? degrees of separation In the Kevin Bacon Game, it is postulated that the center of the Hollywood universe is Kevin Bacon. ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.2/64 Six? degrees of separation In the Kevin Bacon Game, it is postulated that the center of the Hollywood universe is ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.2/64 Six? degrees of separation In the Kevin Bacon Game, it is postulated that the center of the Hollywood universe is Kevin Bacon. This is false. It is Dennis Hopper. ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.2/64 Six? degrees of separation In the Kevin Bacon Game, it is postulated that the center of the Hollywood universe is Kevin Bacon. This is false. It is Dennis Hopper. ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.2/64 Six? degrees of separation In the Kevin Bacon Game, it is postulated that the center of the Hollywood universe is Kevin Bacon. We link two actors together if they appeared together in the same movie. ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.2/64 Six? degrees of separation In the Kevin Bacon Game, it is postulated that the center of the Hollywood universe is Kevin Bacon. We link two actors together if they appeared together in the same movie. (They must be together on a cast list at the IMDb.) The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.2/64 Bacon number The actor’s Bacon number is the fewest number of steps it takes to connect that actor to ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.3/64 Bacon number # The actor’s is the fewest number of steps it takes to connect that actor to Kevin Bacon. ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.3/64 Bacon number The actor’s Bacon number is the fewest number of steps it takes to connect that actor to ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.3/64 Bacon number An actor can have infinite Kevin Bacon number. ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.3/64 Bacon number # An actor can have infinite . (For example, a TV actor who appears in no movie credits.) The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.3/64 Example: Kevin Costner Kevin Costner is linked to Kevin Bacon because both appeared in JFK (1991). ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.4/64 Example: Kevin Costner is linked to because both appeared in ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.4/64 Example: Kevin Costner Kevin Costner is linked to Kevin Bacon because both appeared in JFK (1991). So, Kevin Costner’s Kevin Bacon number is ??? ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.4/64 Example: Kevin Costner Kevin Costner is linked to Kevin Bacon because both appeared in JFK (1991). So, Kevin Costner’s Kevin Bacon number is 1 ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.4/64 Example: Kevin Costner Kevin Costner is linked to Kevin Bacon because both appeared in JFK (1991). # So, ’s is 1 The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.4/64 Illustration: Kevin Costner x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.5/64 Illustration: Kevin Costner x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.5/64 Illustration: Kevin Costner x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.5/64 Illustration: Kevin Costner x x The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.5/64 E.g.: Henry “Fonz” Winkler We know that appeared with in ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.6/64 E.g.: Henry “Fonz” Winkler We know that Henry Winkler appeared with Michael Keaton in Night Shift (1982) appeared with in ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.6/64 E.g.: Henry “Fonz” Winkler We know that Henry Winkler appeared with Michael Keaton in Night Shift (1982) Michael Keaton appeared with Kim Basinger in Batman (1989) appeared with in ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.6/64 E.g.: Henry “Fonz” Winkler We know that Henry Winkler appeared with Michael Keaton in Night Shift (1982) Michael Keaton appeared with Kim Basinger in Batman (1989) Kim Basinger appeared with Mickey Rourke in 9 1/2 Weeks (1986) appeared with in ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.6/64 E.g.: Henry “Fonz” Winkler We know that Henry Winkler appeared with Michael Keaton in Night Shift (1982) Michael Keaton appeared with Kim Basinger in Batman (1989) Kim Basinger appeared with Mickey Rourke in 9 1/2 Weeks (1986) Mickey Rourke appeared with Kevin Bacon in Diner (1982) The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.6/64 A chain: Henry “Fonz” Winkler x x x x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.7/64 A chain: Henry “Fonz” Winkler x x x x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.7/64 A chain: Henry “Fonz” Winkler x x x x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.7/64 A chain: Henry “Fonz” Winkler x x x x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.7/64 A chain: Henry “Fonz” Winkler x x x x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.7/64 A chain: Henry “Fonz” Winkler x x x x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.7/64 A chain: Henry “Fonz” Winkler x x x x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.7/64 A chain: Henry “Fonz” Winkler x x x x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.7/64 A chain: Henry “Fonz” Winkler x x x x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.7/64 A chain: Henry “Fonz” Winkler x x x x x The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.7/64 More: Henry “Fonz” Winkler But it is also true that appeared with ??? in . ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.8/64 More: Henry “Fonz” Winkler But it is also true that appeared with in . ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.8/64 More: Henry “Fonz” Winkler But it is also true that Henry Winkler appeared with Clint Howard in Little Nicky (2000). appeared with in ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.8/64 More: Henry “Fonz” Winkler But it is also true that Henry Winkler appeared with Clint Howard in Little Nicky (2000). Clint Howard appeared with Kevin Bacon in My Dog Skip (2000). The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.8/64 Better: Henry “Fonz” Winkler x x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.9/64 Better: Henry “Fonz” Winkler x x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.9/64 Better: Henry “Fonz” Winkler x x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.9/64 Better: Henry “Fonz” Winkler x x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.9/64 Better: Henry “Fonz” Winkler x x x ▽The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.9/64 Better: Henry “Fonz” Winkler x x x The small world problem: Kevin Bacon, Paul Erdos,˝ William McKinley, and me – 5 degrees of graph theory – p.9/64 Can we do even better? has never appeared in a film with .
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