By Alan Tucker

ISBN-10: 0470458380

ISBN-13: 9780470458389

This is often Alan Tuckers textbook on combinatorics and graph concept

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Additional info for Applied Combinatorics (6th Edition)

Example text

Then (d, e) must go outside. 19b. 20a, is nonplanar. The notation K 3,3 indicates that this graph is a complete bipartite graph consisting of two sets of three vertices with each vertex in one set adjacent to all vertices in the other set. Applying the circle–chord method, we form a circuit containing all six vertices in K 3,3 , and then try to add the remaining edges (not in the circuit) as inside and outside chords. There are several choices for a 6-vertex circuit. 20b. Next the edges (1, 5), (2, 6), and (3, 4) must be added.

We say that a graph is planar if it can be drawn on a plane without edges crossing. We use the term plane graph to refer to a planar depiction of a planar graph. 17 are both planar. 17b is a plane graph. 17b. Our principal focus in this section is determining whether a graph is planar. We take two approaches, both based on the AC Principle. The first approach involves a systematic method for trying to draw a graph edge-by-edge with no crossing edges, in the same spirit as when we tried to determine if two graphs are isomorphic.

There used to be 26 football teams in the National Football League (NFL) with 13 teams in each of two conferences (each conference was divided into divisions, but that is irrelevant here). An NFL guideline said that each team’s 14-game schedule should include exactly 11 games against teams in its own conference and three games against teams in the other conference. By considering the right P1: PBU/OVY P2: PBU/OVY WB00623-01 WB00623-Tucker 30 QC: PBU/OVY T1: PBU November 24, 2011 10:26 Chapter 1 Elements of Graph Theory part of a graph model of this scheduling problem, show that this guideline could not be satisfied!