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Start Over Descriptor "*PATHS & cycles in graph theory" Topic graph connectivity Journal acta mathematica hungarica Publisher springer nature

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1 results on '"*PATHS & cycles in graph theory"'

1. On conjectures and problems of Ruzsa concerning difference graphs of S-units.

Author

Ćustić, A., Hajdu, L., Kreso, D., and Tijdeman, R.

Subjects
*GRAPH theory, *PROBLEM solving, *SET theory, *PATHS & cycles in graph theory, *EXISTENCE theorems, *GRAPH connectivity
Abstract

Given a finite nonempty set of primes S, we build a graph $${\mathcal{G}}$$ with vertex set $${\mathbb{Q}}$$ by connecting $${x, y \in \mathbb{Q}}$$ if the prime divisors of both the numerator and denominator of x − y are from S. In this paper we resolve two conjectures posed by Ruzsa concerning the possible sizes of induced nondegenerate cycles of $${\mathcal{G}}$$ , and also a problem of Ruzsa concerning the existence of subgraphs of $${\mathcal{G}}$$ which are not induced subgraphs. [ABSTRACT FROM AUTHOR]

Published
2015
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