The size of uniquely colorable graphs

  title={The size of uniquely colorable graphs},
  author={Xu Shaoji},
  journal={Journal of Combinatorial Theory, Series B},
  • Xu Shaoji
  • Published 1 December 1990
  • Mathematics
  • Journal of Combinatorial Theory, Series B
Algebraic characterization of uniquely vertex colorable graphs
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It is proved that ( k  − 1) n is a sharp lower bound for the number of edges of a uniquely k -colorable, noncomplete Cayley graph over an abelian group of order n.
Constructions of Uniquely 3-Colorable Graphs
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    2016 IEEE First International Conference on Data Science in Cyberspace (DSC)
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This paper gives a simple counterexample on 16 vertices to S J Xu's conjecture concerning uniquely 3-colorable graphs without triangles, and based on this graph they construct an infinite family of uniquely3- colorable, 4-regular and triangle-free graphs by their construction methods.
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The famous four color theorem states that for all planar graphs, every vertex can be assigned one of 4 colors such that no two adjacent vertices receive the same color. Since Francis Guthrie first


Uniquely colorable graphs