Geodesic
A new approach to chordal graphs
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 465-471.

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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.
Classification : 03C65, 05C38, 05C75
Keywords: connected chordal graph; ternary system 
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Nebeský, Ladislav. A new approach to chordal graphs. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 465-471. http://geodesic.mathdoc.fr/item/CMJ_2007__57_1_a34/