On Uniquely 4-Colorable Planar Graphs
A k-chromatic graph G is called uniquely k-colorable if every k-coloring of the vertex set V of G induces the same partition of V into k color classes. There is an innnite class C of uniquely…
Uniquely colorable Cayley graphs
- MathematicsArs Math. Contemp.
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.
On Uniquely 3-Colorable Plane Graphs without Adjacent Faces of Prescribed Degrees
A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up to the permutation of the colors. For a plane graph G, two faces f 1 and f 2 of G are adjacent ( i…
On the existence of uniquely partitionable graphs
- MathematicsElectron. Notes Discret. Math.
A relation between choosability and uniquely list colorability
- MathematicsJ. Comb. Theory, Ser. B
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