| Title:
|
The all-paths transit function of a graph (English) |
| Author:
|
Changat, Manoj |
| Author:
|
Klavžar, Sandi |
| Author:
|
Mulder, Henry Martyn |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
439-448 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A transit function $R$ on a set $V$ is a function $R\:V\times V\rightarrow 2^{V}$ satisfying the axioms $u\in R(u,v)$, $R(u,v)=R(v,u)$ and $R(u,u)=\lbrace u\rbrace $, for all $u,v \in V$. The all-paths transit function of a connected graph is characterized by transit axioms. (English) |
| Keyword:
|
all-paths convexity |
| Keyword:
|
transit function |
| Keyword:
|
block graph |
| MSC:
|
05C12 |
| MSC:
|
05C75 |
| MSC:
|
05C99 |
| idZBL:
|
Zbl 0977.05135 |
| idMR:
|
MR1844322 |
| . |
| Date available:
|
2009-09-24T10:44:00Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127659 |
| . |
| Reference:
|
[1] P. Duchet: Convexity in combinatorial structures.Rend. Circ. Mat. Palermo (2) Suppl. 14 (1987), 261–293. Zbl 0644.52001, MR 0920860 |
| Reference:
|
[2] P. Duchet: Convex sets in graphs II. Minimal path convexity.J. Combin. Theory Ser. B 44 (1988), 307–316. Zbl 0672.52001, MR 0941439, 10.1016/0095-8956(88)90039-1 |
| Reference:
|
[3] J. Calder: Some elementary properties of interval convexities.J. London Math. Soc. 3 (1971), 422–428. Zbl 0228.52001, MR 0288664, 10.1112/jlms/s2-3.3.422 |
| Reference:
|
[4] M. Farber and R. E. Jamison: Convexity in graphs and hypergraphs.SIAM J. Algebraic Discrete Methods 7 (1986), 433–444. MR 0844046, 10.1137/0607049 |
| Reference:
|
[5] S. Klavžar and H. M. Mulder: Median graphs: characterizations, location theory and related structures.J. Combin. Math. Combin. Comput. 30 (1999), 103–127. MR 1705337 |
| Reference:
|
[6] H. M. Mulder: The Interval Function of a Graph.Mathematical Centre Tracts 132, Mathematisch Centrum, Amsterdam, 1980. Zbl 0446.05039, MR 0605838 |
| Reference:
|
[7] H. M. Mulder: Transit functions on graphs.In preparation. Zbl 1166.05019 |
| Reference:
|
[8] M. A. Morgana and H. M. Mulder: The induced path convexity, betweenness, and svelte graphs.Discrete Math (to appear). MR 1910118 |
| Reference:
|
[9] L. Nebeský: A characterization of the interval function of a connected graph.Czechoslovak Math. J. 44(119) (1994), 173–178. MR 1257943 |
| Reference:
|
[10] L. Nebeský: Characterizing the interval function of a connected graph.Math. Bohem. 123(2) (1998), 137–144. MR 1673965 |
| Reference:
|
[11] E. Sampathkumar: Convex sets in graphs.Indian J. Pure Appl. Math. 15 (1984), 1065–1071. MR 0765010 |
| Reference:
|
[12] M. L. J. van de Vel: Theory of Convex Structures.North Holland, Amsterdam, 1993. MR 1234493 |
| . |
