Abstract
By a chordal graph is meant a graph with no induced cycle of length ⩾ 4. By a ternary system is meant an ordered pair (W, T), where W is a finite nonempty set, and T ⊆ W × W × 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.
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References
G. Chartrand and L. Lesniak: Graphs & Digraphs. Third edition. Chapman & Hall, London, 1996.
R. Diestel: Graph Theory. Second Edition. Graduate Texts in Mathematics 173. Springer, New York, 2000.
G. A. Dirac: On rigid circuit graphs. Abh. Math. Univ. Hamburg 25 (1961), 71–76.
L. Nebeský: Signpost systems and connected graphs. Czech. Math. J. 55 (2005), 283–293.
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Nebeský, L. A new approach to chordal graphs. Czech Math J 57, 465–471 (2007). https://doi.org/10.1007/s10587-007-0073-5
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DOI: https://doi.org/10.1007/s10587-007-0073-5