Generalized edge-chromatic numbers and additive hereditary properties of graphs

Michael J. Dorfling; Samantha Dorfling

Discussiones Mathematicae Graph Theory (2002)

  • Volume: 22, Issue: 2, page 349-359
  • ISSN: 2083-5892

Abstract

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An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. Let and be hereditary properties of graphs. The generalized edge-chromatic number ρ ' ( ) is defined as the least integer n such that ⊆ n. We investigate the generalized edge-chromatic numbers of the properties → H, ₖ, ₖ, *ₖ, ₖ and ₖ.

How to cite

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Michael J. Dorfling, and Samantha Dorfling. "Generalized edge-chromatic numbers and additive hereditary properties of graphs." Discussiones Mathematicae Graph Theory 22.2 (2002): 349-359. <http://eudml.org/doc/270282>.

@article{MichaelJ2002,
abstract = {An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. Let and be hereditary properties of graphs. The generalized edge-chromatic number $ρ^\{\prime \}_\{\}()$ is defined as the least integer n such that ⊆ n. We investigate the generalized edge-chromatic numbers of the properties → H, ₖ, ₖ, *ₖ, ₖ and ₖ.},
author = {Michael J. Dorfling, Samantha Dorfling},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {property of graphs; additive; hereditary; generalized edge-chromatic number},
language = {eng},
number = {2},
pages = {349-359},
title = {Generalized edge-chromatic numbers and additive hereditary properties of graphs},
url = {http://eudml.org/doc/270282},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Michael J. Dorfling
AU - Samantha Dorfling
TI - Generalized edge-chromatic numbers and additive hereditary properties of graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2002
VL - 22
IS - 2
SP - 349
EP - 359
AB - An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. Let and be hereditary properties of graphs. The generalized edge-chromatic number $ρ^{\prime }_{}()$ is defined as the least integer n such that ⊆ n. We investigate the generalized edge-chromatic numbers of the properties → H, ₖ, ₖ, *ₖ, ₖ and ₖ.
LA - eng
KW - property of graphs; additive; hereditary; generalized edge-chromatic number
UR - http://eudml.org/doc/270282
ER -

References

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  1. [1] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, A survey of hereditary properties of graphs, Discuss. Math. Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037. Zbl0902.05026
  2. [2] M. Borowiecki and M. Hałuszczak, Decompositions of some classes of graphs, Report No. IM-3-99 (Institute of Mathematics, Technical University of Zielona Góra, 1999). Zbl0958.05112
  3. [3] I. Broere and M. J. Dorfling, The decomposability of additive hereditary properties of graphs, Discuss. Math. Graph Theory 20 (2000) 281-291, doi: 10.7151/dmgt.1127. Zbl0982.05082
  4. [4] I. Broere, M.J. Dorfling, J.E Dunbar and M. Frick, A path(ological) partition problem, Discuss. Math. Graph Theory 18 (1998) 113-125, doi: 10.7151/dmgt.1068. Zbl0912.05048
  5. [5] I. Broere, S. Dorfling and E. Jonck, Generalized chromatic numbers and additive hereditary properties of graphs, Discuss. Math. Graph Theory 22 (2002) 259-270, doi: 10.7151/dmgt.1174. Zbl1030.05038
  6. [6] J. Nesetril and V. Rödl, Simple proof of the existence of restricted Ramsey graphs by means of a partite construction, Combinatorica 1 (2) (1981) 199-202, doi: 10.1007/BF02579274. Zbl0491.05044

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