| Title:
|
A new approach to chordal graphs (English) |
| Author:
|
Nebeský, Ladislav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
465-471 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
connected chordal graph |
| Keyword:
|
ternary system |
| MSC:
|
03C65 |
| MSC:
|
05C38 |
| MSC:
|
05C75 |
| idZBL:
|
Zbl 1174.05110 |
| idMR:
|
MR2309978 |
| . |
| Date available:
|
2009-09-24T11:47:06Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128184 |
| . |
| Reference:
|
[1] G. Chartrand and L. Lesniak: Graphs & Digraphs.Third edition. Chapman & Hall, London, 1996. MR 1408678 |
| Reference:
|
[2] R. Diestel: Graph Theory.Second Edition. Graduate Texts in Mathematics 173. Springer, New York, 2000. Zbl 0957.05001, MR 1743598 |
| Reference:
|
[3] G. A. Dirac: On rigid circuit graphs.Abh. Math. Univ. Hamburg 25 (1961), 71–76. Zbl 0098.14703, MR 0130190, 10.1007/BF02992776 |
| Reference:
|
[4] L. Nebeský: Signpost systems and connected graphs.Czech. Math. J. 55 (2005), 283–293. MR 2137138, 10.1007/s10587-005-0022-0 |
| . |
