Graph Theory

  • John M. Harris
  • Jeffry L. Hirst
  • Michael J. Mossinghoff
Part of the Undergraduate Texts in Mathematics book series (UTM)


The Pregolya River passes through a city once known as Königsberg. In the 1700s seven bridges were situated across this river (Figure 1.1), and no resident of the city was ever able to walk a route that crossed each of these bridges exactly once. In 1736 the Swiss mathematician Leonhard Euler gave a proof that no such route existed, and his work on the “Königsberg Bridge Problem” is considered by many to be the beginning of the field of graph theory.


Span Tree Bipartite Graph Planar Graph Perfect Match Chromatic Number 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • John M. Harris
    • 1
  • Jeffry L. Hirst
    • 2
  • Michael J. Mossinghoff
    • 3
  1. 1.Department of MathematicsFurman UniversityGreenvilleUSA
  2. 2.Department of MathematicsAppalachian State UniversityBooneUSA
  3. 3.Department of MathematicsUCLALos AngelesUSA

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