MAT4323

From Department of Mathematics at UTSA
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Catalog entry

Prerequisite: Algebra and Number Systems (MAT 1313), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.

Contents (1) Graph models: Isomorphisms, edge counting, planar graphs. (2) Covering circuits and graph colorings: Euler circuits, Hamilton circuits, graph colorings. (3) Network algorithms: Shortest path, minimum spanning trees, matching algorithms, transportation problems. (4) Ramsey's Theorem and Ramsey numbers.

Sample textbooks

[1] Vladlen Koltun, Discrete Structures, Lecture Notes, Stanford University, 2008. Freely available online here

[2] Alan Tucker, Applied Combinatorics, Freely available online here

[3] Gary Chartrand and Ping Zhang, A First Course in Graph Theory, Dover Books on Mathematics, 2012.






Topics List

Week Topic Sections from Tucker's book Subtopics Prerequisite
1-2 Basic counting principles 5.1-5.5 Permutations, combinations, binomial coefficients, arrangements with repetitions MAT1313, CS2233/2231, or instructor consent.
3 Inclusion-Exclusion Principle 8.1-8.2 Counting with Venn diagrams.
1-3 Graph models 12.1-12.3 Isomorphism, edge counting, planar graphs.
4-6 Covering circuits 2.1-2.4 Euler circuits, Hamilton circuits, graph colorings, coloring theorems.
8-9 Trees 3.1-3.4 Search trees, spanning trees, the Traveling Salesman Problem
10-12 Network algorithms 4.1-4.5 Shortest path , minimum spanning trees, matching algorithms, transportation problems. 13-14 Network algorithms Ramsey's Theorem and Ramsey numbers