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2009 | 29 | 3 | 499-510
Tytuł artykułu

The list linear arboricity of planar graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. An and Wu introduce the notion of list linear arboricity lla(G) of a graph G and conjecture that lla(G) = la(G) for any graph G. We confirm that this conjecture is true for any planar graph having Δ ≥ 13, or for any planar graph with Δ ≥ 7 and without i-cycles for some i ∈ {3,4,5}. We also prove that ⌈½Δ(G)⌉ ≤ lla(G) ≤ ⌈½(Δ(G)+1)⌉ for any planar graph having Δ ≥ 9.
Wydawca
Rocznik
Tom
29
Numer
3
Strony
499-510
Opis fizyczny
Daty
wydano
2009
otrzymano
2008-02-12
poprawiono
2009-01-12
zaakceptowano
2009-04-28
Twórcy
autor
  • College of Mathematics and System Science, Xinjiang University, Urumqi 830046, P.R. China
  • College of Mathematics and System Science, Xinjiang University, Urumqi 830046, P.R. China
Bibliografia
  • [1] J. Akiyama, G. Exoo and F. Harary, Covering and packing in graphs III: Cyclic and acyclic invariants, Math. Slovaca 30 (1980) 405-417.
  • [2] J. Akiyama, G. Exoo and F. Harary, Covering and packing in graphs IV: Linear arboricity, Networks 11 (1981) 69-72, doi: 10.1002/net.3230110108.
  • [3] X. An and B. Wu, List linear arboricity of series-parallel graphs, submitted.
  • [4] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (American Elsevier, New York, Macmillan, London, 1976).
  • [5] O.V. Borodin, On the total colouring of planar graphs, J. Reine Angew. Math. 394 (1989) 180-185, doi: 10.1515/crll.1989.394.180.
  • [6] H. Enomoto and B. Péroche, The linear arboricity of some regular graphs, J. Graph Theory 8 (1984) 309-324, doi: 10.1002/jgt.3190080211.
  • [7] F. Guldan, The linear arboricity of 10 regular graphs, Math. Slovaca 36 (1986) 225-228.
  • [8] F. Harary, Covering and packing in graphs I, Ann. N.Y. Acad. Sci. 175 (1970) 198-205, doi: 10.1111/j.1749-6632.1970.tb56470.x.
  • [9] J.L. Wu, On the linear arboricity of planar graphs, J. Graph Theory 31 (1999) 129-134, doi: 10.1002/(SICI)1097-0118(199906)31:2<129::AID-JGT5>3.0.CO;2-A
  • [10] J.L. Wu, The linear arboricity of series-parallel graphs, Graphs Combin. 16 (2000) 367-372, doi: 10.1007/s373-000-8299-9.
  • [11] J.L. Wu, J.F. Hou and G.Z. Liu, The linear arboricity of planar graphs with no short cycles, Theoretical Computer Science 381 (2007) 230-233, doi: 10.1016/j.tcs.2007.05.003.
  • [12] J.L. Wu and Y.W. Wu, The linear arboricity of planar graphs of maximum degree seven is four, J. Graph Theory 58 (2008) 210-220, doi: 10.1002/jgt.20305.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1460
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