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Preprint Number 2620
2620. Manuel Bodirsky and Santiago Guzmán-Pro The Generic Circular Triangle-Free Graph E-mail: Submission date: 18 April 2024 Abstract: In this paper, we introduce the generic circular triangle-free graph
C_3 and propose a finite axiomatization of its first order theory. In
particular, our main results show that a countable graph G embeds into
C_3 if and only if it is a {K_3, K_1 + 2K_2, K_1+C_5, C_6}-free
graph. As a byproduct of this result, we obtain a geometric characterization of
finite {K_3, K_1 + 2K_2, K_1+C_5, C_6}-free graphs, and the (finite) list
of minimal obstructions of unit Helly circular-arc graphs with independence
number strictly less than three. Mathematics Subject Classification: 05C15, 05C63, 05C62, 05C75, 03C10, 03C35 Keywords and phrases: |
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