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On uniquely 3-colorable graphs II

โœ Scribed by Chong-Yun Chao; Zhibo Chen


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
428 KB
Volume
189
Category
Article
ISSN
0012-365X

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โœฆ Synopsis


In [2], for each non-negative integer k, we constructed a connected graph with (24)2k vertices which is uniquely 3-colorable, regular with degree k+5, and triangle-free. Here, for each positive integer n and each integer r > 5, we construct a connected graph with (26)n .2'-' vertices which is uniquely 3-colorable, regular with degree r, and triangle-free.


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## Abstract The generalized Petersen graph __P__(6__k__ + 3, 2) has exactly 3 Hamiltonian cycles for __k__ โ‰ฅ 0, but for __k__ โ‰ฅ 2 is not uniquely edge colorable. This disproves a conjecture of Greenwell and Kronk [1].