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Volumn 24, Issue 4, 2010, Pages 1399-1440

Combinatorics and geometry of finite and infinite squaregraphs

Author keywords

Circular split system; Isometric embedding; Median graph; Plane graph; Tree

Indexed keywords

FORESTRY; GRAPHIC METHODS; POLYNOMIAL APPROXIMATION;

EID: 79251548577     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/090760301     Document Type: Article
Times cited : (30)

References (61)
  • 1
    • 9344257102 scopus 로고    scopus 로고
    • A triangle-free circle graph with chromatic number 5
    • A. A. AGEEV, A triangle-free circle graph with chromatic number 5, Discrete Math., 152(1996), pp. 295-298.
    • (1996) Discrete Math. , vol.152 , pp. 295-298
    • Ageev, A.A.1
  • 2
    • 9344271496 scopus 로고    scopus 로고
    • Every circle graph of girth at least 5 is 3-colourable
    • A. A. AGEEV, Every circle graph of girth at least 5 is 3-colourable, Discrete Math., 195(1999), pp. 229-233.
    • (1999) Discrete Math. , vol.195 , pp. 229-233
    • Ageev, A.A.1
  • 3
    • 84986468413 scopus 로고
    • Retracts of hypercubes
    • H.-J. BANDELT, Retracts of hypercubes, J. Graph Theory, 8(1984), pp. 501-510.
    • (1984) J. Graph Theory , vol.8 , pp. 501-510
    • Bandelt, H.-J.1
  • 4
    • 0021437832 scopus 로고
    • Networks with Condorcet solutions
    • H.-J. BANDELT, Networks with Condorcet solutions, European J. Oper. Res., 20(1985), pp. 314-326.
    • (1985) European J. Oper. Res. , vol.20 , pp. 314-326
    • Bandelt, H.-J.1
  • 7
    • 0030534240 scopus 로고    scopus 로고
    • Graphs of acyclic cubical complexes
    • H.-J. BANDELT AND V. CHEPOI, Graphs of acyclic cubical complexes, European J. Combin., 17(1996), pp. 113-120.
    • (1996) European J. Combin. , vol.17 , pp. 113-120
    • Bandelt, H.-J.1    Chepoi, V.2
  • 11
    • 0000673494 scopus 로고
    • Reconstructing the shape of a tree from observed dissimilarity data
    • H.-J. BANDELT AND A. DRESS, Reconstructing the shape of a tree from observed dissimilarity data, Adv. in Appl. Math., 7(1986), pp. 309-343.
    • (1986) Adv. in Appl. Math. , vol.7 , pp. 309-343
    • Bandelt, H.-J.1    Dress, A.2
  • 12
    • 34047267637 scopus 로고
    • A canonical decomposition theory for metrics on a finite set
    • H.-J. BANDELT AND A. DRESS, A canonical decomposition theory for metrics on a finite set, Adv. Math., 92(1992), pp. 47-105.
    • (1992) Adv. Math. , vol.92 , pp. 47-105
    • Bandelt, H.-J.1    Dress, A.2
  • 14
    • 0033928911 scopus 로고    scopus 로고
    • Median networks: Speedy construction and greedy reduction, one simulation, and two case studies from human mtDNA
    • H.-J. BANDELT, V. MACAULAY, AND M. RICHARDS, Median networks: Speedy construction and greedy reduction, one simulation, and two case studies from human mtDNA, Mol. Phylogen. Evol., 16(2000), pp. 8-28.
    • (2000) Mol. Phylogen. Evol. , vol.16 , pp. 8-28
    • Bandelt, H.-J.1    Macaulay, V.2    Richards, M.3
  • 15
    • 0039639040 scopus 로고
    • Embedding topological median algebras in products of dendrons
    • H.-J. BANDELT AND M. VAN DE VEL, Embedding topological median algebras in products of dendrons, Proc. London Math. Soc. (3), 58(1989), pp. 439-453.
    • (1989) Proc. London Math. Soc. , vol.58 , Issue.3 , pp. 439-453
    • Bandelt, H.-J.1    Van De Vel, M.2
  • 16
    • 38249024519 scopus 로고
    • From copair hypergraphs to median graphs with latent vertices
    • J. P. BARTHÉLEMY, From copair hypergraphs to median graphs with latent vertices, Discrete Math., 76(1989), pp. 9-28.
    • (1989) Discrete Math. , vol.76 , pp. 9-28
    • Barthélemy, J.P.1
  • 18
    • 0041521496 scopus 로고
    • A generalization of Gilmore's theorem
    • M. Fiedler, ed., Acad. Praha, Prague
    • C. BERGE AND P. DUCHET, A generalization of Gilmore's theorem, in Recent Advances in Graph Theory, M. Fiedler, ed., Acad. Praha, Prague, 1975, pp. 49-55.
    • (1975) Recent Advances in Graph Theory , pp. 49-55
    • Berge, C.1    Duchet, P.2
  • 19
    • 51249181542 scopus 로고
    • On the existence of subalgebras of direct products with prescribed d-fold projections
    • G. BERGMAN, On the existence of subalgebras of direct products with prescribed d-fold projections, Algebra Universalis, 7(1977), pp. 341-356.
    • (1977) Algebra Universalis , vol.7 , pp. 341-356
    • Bergman, G.1
  • 20
    • 84966216059 scopus 로고
    • A ternary operation in distributive lattices
    • G. BIRKHOFF AND S. A. KISS, A ternary operation in distributive lattices, Bull. Amer. Math. Soc., 52(1947), pp. 749-752.
    • (1947) Bull. Amer. Math. Soc. , vol.52 , pp. 749-752
    • Birkhoff, G.1    Kiss, S.A.2
  • 24
    • 77955323903 scopus 로고    scopus 로고
    • Kazhdan and Haagerup properties from the median viewpoint
    • I. CHATTERJI, C. DRUŢU, AND F. HAGLUND, Kazhdan and Haagerup properties from the median viewpoint, Adv. Math., 225(2010), pp. 882-921.
    • (2010) Adv. Math. , vol.225 , pp. 882-921
    • Chatterji, I.1    Druţu, C.2    Haglund, F.3
  • 25
    • 0000367441 scopus 로고    scopus 로고
    • On distances in benzenoid systems
    • V. CHEPOI, On distances in benzenoid systems, J. Chem. Inf. Comput. Sci., 36(1996), pp. 1169-1172.
    • (1996) J. Chem. Inf. Comput. Sci. , vol.36 , pp. 1169-1172
    • Chepoi, V.1
  • 26
    • 0042726121 scopus 로고    scopus 로고
    • Graphs of some CAT (0) complexes
    • V. CHEPOI, Graphs of some CAT (0) complexes, Adv. in Appl. Math., 24(2000), pp. 125-179.
    • (2000) Adv. in Appl. Math. , vol.24 , pp. 125-179
    • Chepoi, V.1
  • 28
    • 37849187097 scopus 로고    scopus 로고
    • Distance and routing labeling schemes for nonpositively curved plane graphs
    • V. CHEPOI, F. DRAGAN, AND Y. VAXÈS, Distance and routing labeling schemes for nonpositively curved plane graphs, J. Algorithms, 61(2006), pp. 1-31.
    • (2006) J. Algorithms , vol.61 , pp. 1-31
    • Chepoi, V.1    Dragan, F.2    Vaxès, Y.3
  • 29
    • 84867959170 scopus 로고    scopus 로고
    • Median problem in some plane triangulations and quadrangulations
    • V. CHEPOI, C. FANCIULLINI, AND Y. VAXÈS, Median problem in some plane triangulations and quadrangulations, Comput. Geom., 27(2004), pp. 193-210.
    • (2004) Comput. Geom. , vol.27 , pp. 193-210
    • Chepoi, V.1    Fanciullini, C.2    Vaxès, Y.3
  • 31
    • 0031193219 scopus 로고    scopus 로고
    • The Wiener index and the Szeged index of benzenoid systems in linear time
    • V. CHEPOI AND S. KLAVŽAR, The Wiener index and the Szeged index of benzenoid systems in linear time, J. Chem. Inf. Comput. Sci., 37(1997), pp. 752-755.
    • (1997) J. Chem. Inf. Comput. Sci. , vol.37 , pp. 752-755
    • Chepoi, V.1    Klavžar, S.2
  • 32
    • 33749306854 scopus 로고
    • Distance-preserving subgraphs of hypercubes
    • Z. DJOKOVIĆ, Distance-preserving subgraphs of hypercubes, J. Combin. Theory Ser. B, 14(1973), pp. 263-267.
    • (1973) J. Combin. Theory Ser. B. , vol.14 , pp. 263-267
    • Djoković, Z.1
  • 33
    • 0000733969 scopus 로고    scopus 로고
    • Some variations on a theme by Buneman
    • A. DRESS, K. T. HUBER, AND V. MOULTON, Some variations on a theme by Buneman, Ann. Combin., 1(1997), pp. 339-352.
    • (1997) Ann. Combin. , vol.1 , pp. 339-352
    • Dress, A.1    Huber, K.T.2    Moulton, V.3
  • 35
    • 33847293505 scopus 로고
    • Gated sets in metric spaces
    • A. DRESS AND R. SCHARLAU, Gated sets in metric spaces, Aequationes Math., 34(1987), pp. 112-120.
    • (1987) Aequationes Math. , vol.34 , pp. 112-120
    • Dress, A.1    Scharlau, R.2
  • 36
    • 0028480062 scopus 로고
    • Arboricity and bipartite subgraph listing algorithms
    • D. EPPSTEIN, Arboricity and bipartite subgraph listing algorithms, Inform. Process. Lett., 51(1994), pp. 207-211.
    • (1994) Inform. Process. Lett. , vol.51 , pp. 207-211
    • Eppstein, D.1
  • 37
    • 13944259485 scopus 로고    scopus 로고
    • The lattice dimension of a graph
    • D. EPPSTEIN, The lattice dimension of a graph, European J. Combin., 26(2005), pp. 585-592.
    • (2005) European J. Combin. , vol.26 , pp. 585-592
    • Eppstein, D.1
  • 38
    • 70350570513 scopus 로고    scopus 로고
    • Manhattan orbifolds
    • D. EPPSTEIN, Manhattan orbifolds, Topol. Appl., 157(2010), pp. 494-507.
    • (2010) Topol. Appl. , vol.157 , pp. 494-507
    • Eppstein, D.1
  • 42
    • 0004257896 scopus 로고
    • Charles Scribner's Sons, New York
    • S. W. GOLOMB, Polyominoes, Charles Scribner's Sons, New York, 1965.
    • (1965) Polyominoes
    • Golomb, S.W.1
  • 44
    • 0002450444 scopus 로고    scopus 로고
    • Simplicité de groupes d'automorphismes d'espaces à courbure négative
    • C. Rourke, I. Rivin, and C. Series, eds., Geom. Topol. Publ., Coventry, UK
    • F. HAGLUND AND F. PAULIN, Simplicité de groupes d'automorphismes d'espaces à courbure négative, in The Epstein Birthday Schrift, Geom. Topol. Monogr. 1, C. Rourke, I. Rivin, and C. Series, eds., Geom. Topol. Publ., Coventry, UK, 1998, pp. 181-248.
    • (1998) The Epstein Birthday Schrift, Geom. Topol. Monogr. , vol.1 , pp. 181-248
    • Haglund, F.1    Paulin, F.2
  • 45
    • 0043223319 scopus 로고
    • A set of independent postulates for cyclic order
    • E. V. HUNTINGTON, A set of independent postulates for cyclic order, Proc. Natl. Acad. Sci. USA, 2(1916), pp. 630-631.
    • (1916) Proc. Natl. Acad. Sci. USA , vol.2 , pp. 630-631
    • Huntington, E.V.1
  • 48
    • 70350590725 scopus 로고    scopus 로고
    • Induced cycles in crossing graphs of median graphs
    • S. KLAVŽAR AND M. KOVŠE, Induced cycles in crossing graphs of median graphs, Discrete Math., 309(2009), pp. 6585-6589.
    • (2009) Discrete Math. , vol.309 , pp. 6585-6589
    • Klavžar, S.1    Kovše, M.2
  • 49
    • 0010669428 scopus 로고
    • On upper bounds for the chromatic numbers of graphs
    • in Russian
    • A. V. KOSTOCHKA, On upper bounds for the chromatic numbers of graphs, Trudy Instituta Mathematiki, 10(1988), pp. 204-226 (in Russian).
    • (1988) Trudy Instituta Mathematiki , vol.10 , pp. 204-226
    • Kostochka, A.V.1
  • 50
    • 10044255454 scopus 로고    scopus 로고
    • Minimal cycle bases of outerplanar graphs
    • J. LEYDOLD AND P. STADLER, Minimal cycle bases of outerplanar graphs, Electron J. Combin., 5(1998), R16.
    • (1998) Electron. J. Combin. , vol.5
    • Leydold, J.1    Stadler, P.2
  • 51
    • 0011309536 scopus 로고
    • The expansion procedure for graphs
    • BI Wissenschaftsverlag, Mannheim, Germany
    • H. M. MULDER, The expansion procedure for graphs, in Contemporary Methods in Graph Theory, BI Wissenschaftsverlag, Mannheim, Germany, 1990, pp. 459-477.
    • (1990) Contemporary Methods in Graph Theory , pp. 459-477
    • Mulder, H.M.1
  • 52
    • 0003291985 scopus 로고
    • The interval function of a graph
    • Mathematisch Centrum, Amsterdam
    • H. M. MULDER, The Interval Function of a Graph, Math. Centre Tracts 132, Mathematisch Centrum, Amsterdam, 1980.
    • (1980) Math. Centre Tracts , vol.132
    • Mulder, H.M.1
  • 53
    • 0039923734 scopus 로고
    • Median graphs and Helly hypergraphs
    • H. M. MULDER AND A. SCHRIJVER, Median graphs and Helly hypergraphs, Discrete Math., 25(1979), pp. 41-50.
    • (1979) Discrete Math. , vol.25 , pp. 41-50
    • Mulder, H.M.1    Schrijver, A.2
  • 54
    • 10844252476 scopus 로고    scopus 로고
    • Cubulating spaces with walls
    • B. NICA, Cubulating spaces with walls, Algebr. Geom. Topol., 4(2004), pp. 297-309.
    • (2004) Algebr. Geom. Topol. , vol.4 , pp. 297-309
    • Nica, B.1
  • 55
    • 0043284228 scopus 로고    scopus 로고
    • Triangle-free graphs with large chromatic numbers
    • A. NILL, Triangle-free graphs with large chromatic numbers, Discrete Math., 211(2000), pp. 261-262.
    • (2000) Discrete Math. , vol.211 , pp. 261-262
    • Nill, A.1
  • 58
    • 0036662502 scopus 로고    scopus 로고
    • A fast algorithm for generating nonisomorphic chord diagrams
    • J. SAWADA, A fast algorithm for generating nonisomorphic chord diagrams, SIAM J. Discrete Math., 15(2002), pp. 546-561.
    • (2002) SIAM J. Discrete Math. , vol.15 , pp. 546-561
    • Sawada, J.1
  • 59
    • 2442636143 scopus 로고    scopus 로고
    • Cyclic permutations and evolutionary trees
    • C. SEMPLE AND M. STEEL, Cyclic permutations and evolutionary trees, Adv. in Appl. Math., 32(2004), pp. 669-680.
    • (2004) Adv. in Appl. Math. , vol.32 , pp. 669-680
    • Semple, C.1    Steel, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.