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We propose a formalization of graph theory in HOL Light. We give some basic definitions and prove some theorems:

  • the chromatic polynomial theorem
  • cardinality properties of connected graphs
  • the sum of the degree of all vertexes is equal to two times the number of edges
  • the Maxflow Mincut theorem

We also present a vertex coloring algorithm and some examples of usage of the functions and algorithms defined in the formalization.

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