Skip to main content
SpringerLink
Log in

Edge-colouring of joins of regular graphs, I

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

We prove that the edges of every even graph G=G 1+G 2 that is the join of two regular graphs G i =(V i ,E i ) can be coloured with Δ(G) colours, whenever Δ(G)=Δ(G 2)+|V 1|. The proof of this result yields a combinatorial algorithm to optimally colour the edges of this type of graphs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Berry R, Modiano E (2005) Optimal transceiver scheduling in WDM/TDM networks. IEEE J Sel Areas Comm 23:1479–1495

    Article  Google Scholar 

  • Burlingham LS, Corneil DG, Lerchs H (1981) Complement reducible graphs. Discrete Appl Math 3:163–174

    Article  MATH  MathSciNet  Google Scholar 

  • Chvátal V (1975) On certain polytopes associated with graphs. J Comb Theory, Ser B 18:138–154

    Article  MATH  Google Scholar 

  • Chetwynd AG, Hilton AJW (1984) The chromatic index of graphs of even order with many edges. J Graph Theory 8:463–470

    Article  MATH  MathSciNet  Google Scholar 

  • Chetwynd AG, Hilton AJW (1989) The edge-chromatic class of graphs with maximum degree at least |V|−3. Ann Discrete Math 41:91–110

    Article  MathSciNet  Google Scholar 

  • De Simone C, Picinin de Mello C (2006) Edge colouring of join graphs. Theor Comp Sci 355:364–370

    Article  MATH  Google Scholar 

  • De Simone C, Galluccio A (2007) Edge-colouring of regular graphs of large degree. Theor Comp Sci 389:91–99

    Article  MATH  Google Scholar 

  • De Simone C, Galluccio A (2009) Edge-colouring of joins of regular graphs, II. Manuscript

  • De Werra D (1972) Investigations on an edge-coloring problem. Discrete Math 1:167–179

    Article  Google Scholar 

  • Hoffman DG, Rodger CA (1992) The chromatic index of complete multipartite graphs. J Graph Theory 16:159–163

    Article  MATH  MathSciNet  Google Scholar 

  • Holyer I (1981) The NP-completeness of edge-colouring. SIAM J Comput 14:718–720

    Article  MathSciNet  Google Scholar 

  • McDiarmid CJH (1972) The solution of a timetabling problem. J Inst Math Appl 9:23–34

    Article  MATH  MathSciNet  Google Scholar 

  • Möhring RH (1985) Algorithmic aspects of the substitution decomposition in optimization over relations, set systems and Boolean functions. Ann Oper Res 4:195–225

    Article  MathSciNet  Google Scholar 

  • Nakano S, Nishizeki T (1993) Scheduling file transfers under port and channel constraints. Int J Found Comput Sci 4:101–115

    Article  MATH  MathSciNet  Google Scholar 

  • Niessen T, Volkmann L (1990) Class 1 conditions depending on the minimum degree and the number of vertices of maximum degree. J Graph Theory 14:225–246

    Article  MATH  MathSciNet  Google Scholar 

  • Niessen T (2001) How to find overfull subgraphs in graphs with large maximum degree, II. Electron J Comb 8:#R7

    MathSciNet  Google Scholar 

  • Padberg M, Rao MR (1982) Odd minimum cutsets and b-matchings. Math Oper Res 7:67–80

    Article  MATH  MathSciNet  Google Scholar 

  • Perkovic L, Reed B (1997) Edge coloring regular graphs of high degree. Discrete Math 165/166:567–570

    Article  MathSciNet  Google Scholar 

  • Perkovic L (1998) Edge coloring, polyhedra and probability. PhD Thesis, Carnegie Mellon University, US

  • Plantholt M (1981) The chromatic class of graphs with a spanning star. J Graph Theory 5:5–13

    Article  MathSciNet  Google Scholar 

  • Vizing VG (1964) On an estimate of the chromatic class of a p-graph. Diskret Anal 3:25–30 (in Russian)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IASI–CNR, viale Manzoni 30, 00185, Rome, Italy

    Caterina De Simone & Anna Galluccio

Authors
  1. Caterina De Simone
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anna Galluccio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anna Galluccio.

Rights and permissions

Reprints and permissions

About this article

Cite this article

De Simone, C., Galluccio, A. Edge-colouring of joins of regular graphs, I. J Comb Optim 18, 417–428 (2009). https://doi.org/10.1007/s10878-009-9235-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-009-9235-8

Keywords

Search

Navigation