On constructible graphs, infinite bridged graphs and weakly cop-win graphs

Discrete Mathematics

Volumn 224, Issue 1-3, 2000, Pages 61-78

  Chastand, Marc ^a   Laviolette, François ^b   Polat, Norbert ^a  

^a UNIVERSITÉ JEAN MOULIN LYON 3   (France)

^b UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Bridged graph; Constructible graph; Dismantlable graph; Dually compact closed class; Helly graph; Infinite graph; Weakly cop win graph

Indexed keywords

EID: 0345754861     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(00)00127-8     Document Type: Article

References (20)

1. R.P. Anstee, M. Farber, On bridged graphs and cop-win graphs, J. Combin. Theory Ser. B 44 (1988) 22-28.
2. H.-J. Bandelt, V. Chepoi, A Helly theorem in weakly modular space, Discrete Math. 160 (1996) 25-39.
3. M. Chastand, Classes de graphes compacts faiblements modulaires, Thèse de doctorat, Université Claude Bernard, Lyon 1, 1997.
4. M. Chastand, N. Polat, Invariant Hamming graphs in infinite quasi-median graphs, Discrete Math. 160 (1996) 93-104.
5. V. Chepoi, Bridged graphs are cop-win graphs: an algorithmic proof, J. Combin. Theory. Ser. B 69 (1997) 97-100.
6. V. Chepoi, Graphs of some CAT(0) complexes, Adv. Appl. Math. 24 (2000) 125-179.
7. M. Farber, R.E. Jamison, On local convexity in graphs, Discrete Math. 66 (1987) 231-247.
8. G. Hahn, F. Laviolette, N. Sauer, R.E. Woodrow, On cop-win graphs, Preprint, 1989.
9. G. Hahn, N. Sauer, R.E. Woodrow, Personal communication.
10. E. Jawhari, D. Misane, M. Pouzet, Retracts: graphs and ordered sets from the metric point of view, Contemp. Math. 57 (1986) 175-226.
11. R. Nowakowski, P. Winkler, Vertex-to-vertex pursuit in a graph, Discrete Math. 43 (1983) 235-239.
12. E. Pesch, Minimal extensions of graphs to absolute retracts, J. Graph Theory 11 (1987) 585-598.
13. N. Polat, Finite invariant simplices in infinite graphs, Period. Math. Hungar 27 (1993) 125-136.
14. N. Polat, Retract-collapsible graphs and invariant subgraph properties, J. Graph Theory 19 (1995) 25-44.
15. N. Polat, Graphs without isometric rays and invariant subgraph properties, I, J. Graph Theory 27 (1998) 99-109.
16. N. Polat, On infinite bridged graphs and strongly dismantlable graphs, Discrete Math. 211 (2000) 153-166.
17. N. Polat, On isometric subgraphs of infinite bridged graphs and geodesic convexity, Discrete Math., to appear.
18. A. Quillot, Thèse de 3e cycle, Université de Paris VI, 1978.
19. V. Soltan, V. Chepoi, Conditions for invariance of set diameters under d-convexification, Cybernetics 19 (1983) 750-756.
20. C. Tardif, On compact median graphs, J. Graph Theory 23 (1996) 325-336.