DM

Discrete Mathematics


Theorems with proofs for the egzam:

   1.       Euler Theorem (with lemma)
   2.       Dirac Theorem
   3.       Characterization of bipartite graphs (no odd circles)
   4.       Euler Formula
   5.       Five color Theorem (Heawood)
   6.       Hall Theorem
   7.       Ford, Fulkerson Theorem
   8.       Dilworth's Theorem.


DM0 - Induction

DM1 - Counting

DM2 - More Counting, Partitions

DM3 - Inclusion-exclusion principle

DM4 - Generatin functions

DM5 - Notation O()

DM6 - Codes

DM7 - Graphs

DM8 - Euler tours, Hamiltonian cycles

DM9 - Graph coloring

DM10 - Planar graphs

Previous tests

test 1: 2006|2006a|2007 | 2008

test2: 2006|2006a

test 3: 2005|2006|2007

test 4: 2005|2006|2007

1) J. A. Bondy, U. S. R. Murty, Graph Theory with Applications, American Elsevier Publishing Co., 1976.
2) W. Lipski, Kombinatoryka dla programistów, Warszawa, WNT 2004.3) W. Lipski, W. Marek, Analiza kombinatoryczna, PWN, 1986.
4)F. Roberts, Applied Combinatorics, Prentice Hall, 1984.
5) K. A. Ross, C.R.B.Wright, Matematyka Dyskretna, PWN 1999.
6) R.J. Wilson, Introduction to Graph Theory, Addison Wesley, 1996.
7) R. Diestel, Graph Theory, Springer-Verlag 1997,2000,2005
http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/GraphTheoryIII.pdf 8)       http://users.utu.fi/harju/graphtheory/graphtheory.html
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