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2016 | 36 | 3 | 523-544
Tytuł artykułu

Cycle Double Covers of Infinite Planar Graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we study the existence of cycle double covers for infinite planar graphs. We show that every infinite locally finite bridgeless k-indivisible graph with a 2-basis admits a cycle double cover.
Słowa kluczowe
Wydawca
Rocznik
Tom
36
Numer
3
Strony
523-544
Opis fizyczny
Daty
wydano
2016-08-01
otrzymano
2014-12-08
poprawiono
2015-05-23
zaakceptowano
2015-08-16
online
2016-07-06
Twórcy
  • 515 Loudon Road School of Science, Siena College Loudonville, NY 12211, USA, mjavaheri@siena.edu
Bibliografia
  • [1] J.C. Bermond, B. Jackson and F. Jaeger, Shortest coverings of graphs with cycles, J. Combin. Theory Ser. B 35 (1993) 297-308. doi:10.1016/0095-8956(83)90056-4[Crossref]
  • [2] G. Brinkmann, J. Goedgebeur, J. Hägglund and K. Markström, Generation and properties of snarks, J. Combin. Theory Ser. B 103 (2013) 468-488. doi:10.1016/j.jctb.2013.05.001[WoS][Crossref]
  • [3] H. Bruhn and M. Stein, MacLane’s planarity criterion for locally finite graphs, J. Combin. Theory Ser. B 96 (2006) 225-239. doi:10.1016/j.jctb.2005.07.005[Crossref]
  • [4] M. Chan, A survey of the cycle double cover conjecture, (2009).
  • [5] N.G. de Bruijn and P. Erdős, A colour problem for infinite graphs and a problem in the theory of relations, Nederl. Akad. Wetensch. Porc. Ser. A 54 (1951) 369-373.
  • [6] R. Diestel, The cycle space of an infinite graph, Combin. Probab. Comput. 14 (2005) 59-79. doi:10.1017/S0963548304006686[Crossref]
  • [7] R. Diestel and D. Kühl, On infinite cycles I, Combinatorica 24 (2004) 69-89. doi:10.1007/s00493-004-0005-z[Crossref]
  • [8] R. Diestel and D. Kühl, On infinite cycles II, Combinatorica 24 (2004) 91-116. doi:10.1007/s00493-004-0006-y[Crossref]
  • [9] G. Fan, Covering graphs by cycles, SIAM J. Discrete Math. 5 (1992) 491-496. doi:10.1137/0405039[Crossref]
  • [10] I. Fary, On straight line representations of planar graphs, Acta Sci. Math. (Szeged) 11 (1984) 229-233.
  • [11] H. Fleischner, Proof of the strong 2-cover conjecture for planar graphs, J. Combin. Theory Ser. B 40 (1986) 229-230. doi:10.1016/0095-8956(86)90080-8[Crossref]
  • [12] H. Fleischner and R. Häggkvist, Circuit double covers in special types of cubic graphs, Discrete Math. 309 (2009) 5724-5728. doi:10.1016/j.disc.2008.05.018[WoS][Crossref]
  • [13] L. Goddyn, A girth requirement for the double cycle cover conjecture, Ann. Discrete Math. 27 (1985) 13-26. doi:10.1016/s0304-0208(08)72994-3[Crossref]
  • [14] J. Hägglund and K. Markström, On stable cycles and cycle double covers of graphs with large circumference, Discrete Math. 312 (2012) 2540-2544. doi:10.1016/j.disc.2011.08.024[WoS][Crossref]
  • [15] A. Hoffmann-Ostenhof, A note on 5-cycle double covers, Graphs Combin. 29 (2013) 977-979. doi:10.1007/s00373-012-1169-8[Crossref]
  • [16] A. Huck, Reducible configurations for the cycle double cover conjecture, Discrete Appl. Math. 99 (2000) 71-90. doi:10.1016/S0166-218X(99)00126-2[Crossref]
  • [17] R. Isaacs, Infinite families of nontrivial trivalent graphs which are not Tait colorable, Amer. Math. Monthly 82 (1975) 221-239. doi:10.2307/2319844[Crossref]
  • [18] F. Jaeger, A survey of the cycle double cover conjecture, Ann. Discrete Math. 27 (1985) 1-12. doi:10.1016/s0304-0208(08)72993-1[Crossref]
  • [19] F. Jaeger, On circular flows in graphs, Proc. Colloq. Math. Janos Bolyai (1982) 391-402.
  • [20] S. MacLane, A combinatorial condition for planar graphs, Fund. Math. 28 (1937) 22-32.
  • [21] P.D. Seymour, Disjoint paths in graphs, Discrete Math. 29 (1980) 293-309. doi:10.1016/0012-365X(80)90158-2[Crossref]
  • [22] P.D. Seymour, Nowhere-zero 6-flows, J. Combin. Theory Ser. B 30 (1981) 130-135. doi:10.1016/0095-8956(81)90058-7[Crossref]
  • [23] G. Szekeres, Polyhedral decompositions of cubic graphs, Bull. Aust. Math. Soc. 8 (1973) 367-387. doi:10.1017/S0004972700042660[Crossref]
  • [24] P.G. Tait, Remarks on the colourings of maps, Proc. Roy. Soc. Edinburgh Sect. A 10 (1880) 729.[Crossref]
  • [25] C. Thomassen, Planarity and duality of finite and infinite graphs, J. Combin. Theory Ser. B 29 (1980) 244-271. doi:10.1016/0095-8956(80)90083-0[Crossref]
  • [26] C. Thomassen, Straight line representation of infinite planar graphs, J. Lond. Math. Soc. (2) 16 (1977) 411-423. doi:10.1112/jlms/s2-16.3.411[Crossref]
  • [27] W.T. Tutte, A contribution to the theory of chromatic polynomials, Canad. J. Math. 6 (1954) 80-91. doi:10.4153/CJM-1954-010-9[Crossref]
  • [28] K. Wagner, Fastplättbare Graphen, J. Combin. Theory 3 (1967) 326-365. doi:10.1016/S0021-9800(67)80103-0[Crossref]
  • [29] R. Xu, Strong 5-cycle double covers of graphs, Graphs Combin. 30 (2014) 495-499. doi:10.1007/s00373-012-1266-8[Crossref]
  • [30] D. Ye, Perfect Matching and Circuit Cover of Graphs (Ph.D. Dissertation, West Virginia University, 2012).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1879
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