Download this article
 Download this article For screen
For printing
Recent Issues

Volume 29
Issue 9, 4477–4945
Issue 8, 3921–4476
Issue 7, 3345–3919
Issue 6, 2783–3343
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Helly groups

Jérémie Chalopin, Victor Chepoi, Anthony Genevois, Hiroshi Hirai and Damian Osajda

Geometry & Topology 29 (2025) 1–70
Bibliography
1 J A Altobelli, The word problem for Artin groups of FC type, J. Pure Appl. Algebra 129 (1998) 1 MR1626651
2 N Aronszajn, P Panitchpakdi, Extension of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6 (1956) 405 MR0084762
3 H J Bandelt, Hereditary modular graphs, Combinatorica 8 (1988) 149 MR0963122
4 H J Bandelt, V Chepoi, Metric graph theory and geometry: a survey, from: "Surveys on discrete and computational geometry" (editors J E Goodman, J Pach, R Pollack), Contemp. Math. 453, Amer. Math. Soc. (2008) 49 MR2405677
5 H J Bandelt, V Chepoi, D Eppstein, Combinatorics and geometry of finite and infinite squaregraphs, SIAM J. Discrete Math. 24 (2010) 1399 MR2735930
6 H J Bandelt, H M Mulder, Pseudomodular graphs, Discrete Math. 62 (1986) 245 MR0866940
7 H J Bandelt, H M Mulder, E Wilkeit, Quasi-median graphs and algebras, J. Graph Theory 18 (1994) 681 MR1297190
8 H J Bandelt, E Pesch, Dismantling absolute retracts of reflexive graphs, European J. Combin. 10 (1989) 211 MR1029165
9 H J Bandelt, E Prisner, Clique graphs and Helly graphs, J. Combin. Theory Ser. B 51 (1991) 34 MR1088625
10 H J Bandelt, M van de Vel, Superextensions and the depth of median graphs, J. Combin. Theory Ser. A 57 (1991) 187 MR1111556
11 J A Barmak, E G Minian, Strong homotopy types, nerves and collapses, Discrete Comput. Geom. 47 (2012) 301 MR2872540
12 A Bartels, W Lück, The Borel conjecture for hyperbolic and CAT(0)-groups, Ann. of Math. 175 (2012) 631 MR2993750
13 C Berge, Hypergraphs: combinatorics of finite sets, 45, North-Holland (1989) MR1013569
14 C Berge, P Duchet, A generalization of Gilmore’s theorem, from: "Recent advances in graph theory" (editor M Fiedler), Academia (1975) 49 MR0406801
15 C Berge, M Las Vergnas, Sur un théorème du type König pour hypergraphes, Ann. New York Acad. Sci. 175 (1970) 32 MR0266787
16 M Bestvina, Local homology properties of boundaries of groups, Michigan Math. J. 43 (1996) 123 MR1381603
17 A Björner, Topological methods, from: "Handbook of combinatorics, II" (editors R L Graham, M Grötschel, L Lovász), Elsevier (1995) 1819 MR1373690
18 K Borsuk, On the imbedding of systems of compacta in simplicial complexes, Fund. Math. 35 (1948) 217 MR0028019
19 B H Bowditch, Median and injective metric spaces, Math. Proc. Cambridge Philos. Soc. 168 (2020) 43 MR4043820
20 T Brady, J P McCammond, Three-generator Artin groups of large type are biautomatic, J. Pure Appl. Algebra 151 (2000) 1 MR1770639
21 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
22 P J Cameron, Dual polar spaces, Geom. Dedicata 12 (1982) 75 MR0645040
23 J Chalopin, V Chepoi, H Hirai, D Osajda, Weakly modular graphs and nonpositive curvature, 1309, Amer. Math. Soc. (2020) MR4223822
24 R Charney, Artin groups of finite type are biautomatic, Math. Ann. 292 (1992) 671 MR1157320
25 V D Chepoi, Classification of graphs by means of metric triangles, Metody Diskret. Analiz. (1989) 75 MR1114014
26 V Chepoi, A note on r-dominating cliques, Discrete Math. 183 (1998) 47 MR1606788
27 V Chepoi, Graphs of some CAT(0) complexes, Adv. in Appl. Math. 24 (2000) 125 MR1748966
28 V Chepoi, F F Dragan, B Estellon, M Habib, Y Vaxès, Diameters, centers, and approximating trees of δ-hyperbolic geodesic spaces and graphs, from: "Symposium on computational geometry", ACM (2008) 59 MR2504271
29 V Chepoi, B Estellon, Packing and covering δ-hyperbolic spaces by balls, from: "Approximation, randomization, and combinatorial optimization: algorithms and techniques" (editors M Charikar, K Jansen, O Reingold, J D P Rolim), Lecture Notes in Comput. Sci. 4627, Springer (2007) 59
30 V Chepoi, K Knauer, T Marc, Hypercellular graphs : partial cubes without Q3 as partial cube minor, Discrete Math. 343 (2020) 111678 MR4065838
31 M Chrobak, L L Larmore, Generosity helps or an 11-competitive algorithm for three servers, J. Algorithms 16 (1994) 234 MR1258238
32 D Descombes, Asymptotic rank of spaces with bicombings, Math. Z. 284 (2016) 947 MR3563261
33 D Descombes, U Lang, Convex geodesic bicombings and hyperbolicity, Geom. Dedicata 177 (2015) 367 MR3370039
34 D Descombes, U Lang, Flats in spaces with convex geodesic bicombings, Anal. Geom. Metr. Spaces 4 (2016) 68 MR3483604
35 F F Dragan, Центры в графах и своıство Хелли, PhD thesis, Moldova State University (1989)
36 F F Dragan, H M Guarnera, Obstructions to a small hyperbolicity in Helly graphs, Discrete Math. 342 (2019) 326 MR3873004
37 A W M Dress, Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: a note on combinatorial properties of metric spaces, Adv. Math. 53 (1984) 321 MR0753872
38 A W M Dress, A note on compact groups, acting on -trees, Beitr. Algebra Geom. 29 (1989) 81 MR1036092
39 A W M Dress, R Scharlau, Gated sets in metric spaces, Aequationes Math. 34 (1987) 112 MR915878
40 D B A Epstein, J W Cannon, D F Holt, S V F Levy, M S Paterson, W P Thurston, Word processing in groups, Jones & Bartlett (1992) MR1161694
41 F Escalante, Über iterierte Clique-Graphen, Abh. Math. Sem. Univ. Hamburg 39 (1973) 59 MR0329947
42 M Farber, R E Jamison, On local convexity in graphs, Discrete Math. 66 (1987) 231 MR0900046
43 F T Farrell, J F Lafont, EZ-structures and topological applications, Comment. Math. Helv. 80 (2005) 103 MR2130569
44 T Fukaya, S i Oguni, A coarse Cartan–Hadamard theorem with application to the coarse Baum–Connes conjecture, J. Topol. Anal. 12 (2020) 857 MR4139217
45 A Genevois, Cubical-like geometry of quasi-median graphs and applications to geometric group theory, PhD thesis, Aix-Marseille Université (2017) arXiv:1712.01618
46 R Geoghegan, Topological methods in group theory, 243, Springer (2008) MR2365352
47 S M Gersten, H B Short, Small cancellation theory and automatic groups, Invent. Math. 102 (1990) 305 MR1074477
48 O Goodman, V Moulton, On the tight span of an antipodal graph, Discrete Math. 218 (2000) 73 MR1754328
49 M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR0919829
50 V S Guba, M V Sapir, On subgroups of the R Thompson group F and other diagram groups, Mat. Sb. 190 (1999) 3 MR1725439
51 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
52 P Hell, I Rival, Absolute retracts and varieties of reflexive graphs, Canad. J. Math. 39 (1987) 544 MR0905743
53 S Hensel, D Osajda, P Przytycki, Realisation and dismantlability, Geom. Topol. 18 (2014) 2079 MR3268774
54 N Hoda, Quadric complexes, Michigan Math. J. 69 (2020) 241 MR4104372
55 N Hoda, Crystallographic Helly groups, Bull. Lond. Math. Soc. 55 (2023) 2991
56 J Huang, D Osajda, Large-type Artin groups are systolic, Proc. Lond. Math. Soc. 120 (2020) 95 MR3999678
57 J Huang, D Osajda, Helly meets Garside and Artin, Invent. Math. 225 (2021) 395 MR4285138
58 S Hughes, M Valiunas, Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity, (2022) arXiv:2203.11996
59 J R Isbell, Six theorems about injective metric spaces, Comment. Math. Helv. 39 (1964) 65 MR0182949
60 J R Isbell, Median algebra, Trans. Amer. Math. Soc. 260 (1980) 319 MR0574784
61 T Januszkiewicz, J Świątkowski, Simplicial nonpositive curvature, Publ. Math. Inst. Hautes Études Sci. 104 (2006) 1 MR2264834
62 E M Jawhari, M Pouzet, D Misane, Retracts: graphs and ordered sets from the metric point of view, from: "Combinatorics and ordered sets" (editor I Rival), Contemp. Math. 57, Amer. Math. Soc. (1986) 175 MR0856237
63 M Kapovich, B Leeb, On asymptotic cones and quasi-isometry classes of fundamental groups of 3-manifolds, Geom. Funct. Anal. 5 (1995) 582 MR1339818
64 D Kasprowski, H Rüping, The Farrell–Jones conjecture for hyperbolic and CAT(0)-groups revisited, J. Topol. Anal. 9 (2017) 551 MR3684616
65 U Lang, Injective hulls of certain discrete metric spaces and groups, J. Topol. Anal. 5 (2013) 297 MR3096307
66 L Lovász, Combinatorial problems and exercises, North-Holland (1979) 551 MR0537284
67 R C Lyndon, P E Schupp, Combinatorial group theory, 89, Springer (1977) MR577064
68 B Miesch, Gluing hyperconvex metric spaces, Anal. Geom. Metr. Spaces 3 (2015) 102 MR3349339
69 G A Niblo, L D Reeves, The geometry of cube complexes and the complexity of their fundamental groups, Topology 37 (1998) 621 MR1604899
70 D Osajda, Residually finite non-exact groups, Geom. Funct. Anal. 28 (2018) 509 MR3788209
71 D Osajda, Small cancellation labellings of some infinite graphs and applications, Acta Math. 225 (2020) 159 MR4176066
72 D Osajda, T Prytuła, Classifying spaces for families of subgroups for systolic groups, Groups Geom. Dyn. 12 (2018) 1005 MR3845715
73 D Osajda, P Przytycki, Boundaries of systolic groups, Geom. Topol. 13 (2009) 2807 MR2546621
74 D Peifer, Artin groups of extra-large type are biautomatic, J. Pure Appl. Algebra 110 (1996) 15 MR1390670
75 E Pesch, Minimal extensions of graphs to absolute retracts, J. Graph Theory 11 (1987) 585 MR0917206
76 E Pesch, Retracts of graphs, 110, Athenäum (1988) MR0930269
77 N Polat, Finite invariant simplices in infinite graphs, Period. Math. Hungar. 27 (1993) 125 MR1291160
78 N Polat, Convexity and fixed-point properties in Helly graphs, Discrete Math. 229 (2001) 197 MR1815607
79 S J Pride, On Tits’ conjecture and other questions concerning Artin and generalized Artin groups, Invent. Math. 86 (1986) 347 MR0856848
80 A Quilliot, On the Helly property working as a compactness criterion on graphs, J. Combin. Theory Ser. A 40 (1985) 186 MR0804883
81 M Roller, Poc sets, median algebras and group actions, Habilitationsschrift, Universität Regensburg (1998) arXiv:1607.07747
82 M Sageev, Ends of group pairs and non-positively curved cube complexes, Proc. Lond. Math. Soc. 71 (1995) 585 MR1347406
83 J P Serre, Trees, Springer (1980) MR607504
84 V P Soltan, V D Chepoi, Conditions for invariance of set diameters under d-convexification in a graph, Kibernetika (Kiev) (1983) 14 MR765117
85 J Świątkowski, Regular path systems and (bi)automatic groups, Geom. Dedicata 118 (2006) 23 MR2239447
86 J L Szwarcfiter, Recognizing clique-Helly graphs, Ars Combin. 45 (1997) 29 MR1447758
87 M van de Vel, Collapsible polyhedra and median spaces, Proc. Amer. Math. Soc. 126 (1998) 2811 MR1452832
88 D T Wise, Cubulating small cancellation groups, Geom. Funct. Anal. 14 (2004) 150 MR2053602