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Keywords:
connected chordal graph; ternary system
connected chordal graph; ternary system
Summary:
By a chordal graph is meant a graph with no induced cycle of length $\ge 4$. By a ternary system is meant an ordered pair $(W, T)$, where $W$ is a finite nonempty set, and $T \subseteq W \times W \times W$. Ternary systems satisfying certain axioms (A1)–(A5) are studied in this paper; note that these axioms can be formulated in a language of the first-order logic. For every finite nonempty set $W$, a bijective mapping from the set of all connected chordal graphs $G$ with $V(G) = W$ onto the set of all ternary systems $(W, T)$ satisfying the axioms (A1)–(A5) is found in this paper.
References:
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[4] L. Nebeský: Signpost systems and connected graphs. Czech. Math. J. 55 (2005), 283–293. DOI 10.1007/s10587-005-0022-0 | MR 2137138
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