On a question concerning prime distance graphs

Authors:
V. Yegnanarayanan
Affiliations:
Department of Science and Humanities, Arulmigu Meenakshi Amman College of Engineering, Vadamavandal, Kanchipuram, TN, India
Venue:
Discrete Mathematics
Year:
2002

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Abstract

Let D be a subset of the set P of prime numbers not containing any twin primes. Kemnitz and Kolberg raised the following question. For any given natural number n, are there only finitely many such minimal sets D, of the size n, such that the induced prime distance graph has chromatic number 4? In this paper, a conditional answer to this question based on a well-known conjecure from the prime number theory is given.