# Some maximum multigraphs and edge/vertex distance colourings

Discussiones Mathematicae Graph Theory (1995)

- Volume: 15, Issue: 1, page 89-106
- ISSN: 2083-5892

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topZdzisław Skupień. "Some maximum multigraphs and edge/vertex distance colourings." Discussiones Mathematicae Graph Theory 15.1 (1995): 89-106. <http://eudml.org/doc/270722>.

@article{ZdzisławSkupień1995,

abstract = {Shannon-Vizing-type problems concerning the upper bound for a distance chromatic index of multigraphs G in terms of the maximum degree Δ(G) are studied. Conjectures generalizing those related to the strong chromatic index are presented. The chromatic d-index and chromatic d-number of paths, cycles, trees and some hypercubes are determined. Among hypercubes, however, the exact order of their growth is found.},

author = {Zdzisław Skupień},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {(strong) chromatic index; chromatic number; matching; hypercube; error-correcting code; asymptotics; distance colourings; chromatic index; multigraph; line graph; maximum degree; trees; cycles},

language = {eng},

number = {1},

pages = {89-106},

title = {Some maximum multigraphs and edge/vertex distance colourings},

url = {http://eudml.org/doc/270722},

volume = {15},

year = {1995},

}

TY - JOUR

AU - Zdzisław Skupień

TI - Some maximum multigraphs and edge/vertex distance colourings

JO - Discussiones Mathematicae Graph Theory

PY - 1995

VL - 15

IS - 1

SP - 89

EP - 106

AB - Shannon-Vizing-type problems concerning the upper bound for a distance chromatic index of multigraphs G in terms of the maximum degree Δ(G) are studied. Conjectures generalizing those related to the strong chromatic index are presented. The chromatic d-index and chromatic d-number of paths, cycles, trees and some hypercubes are determined. Among hypercubes, however, the exact order of their growth is found.

LA - eng

KW - (strong) chromatic index; chromatic number; matching; hypercube; error-correcting code; asymptotics; distance colourings; chromatic index; multigraph; line graph; maximum degree; trees; cycles

UR - http://eudml.org/doc/270722

ER -

## References

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- [6] P. Horák, H. Qing and W.T. Trotter, Induced matchings in cubic graphs, J. Graph Theory 17 (1993) 151-160. [Communicated at 1991 Conf. in Zemplinska Sirava (CS).], doi: 10.1002/jgt.3190170204. Zbl0787.05038
- [7] F. Kramer, Sur le nombre chromatique K(p,G) des graphes, Rev. Franç. Automat. Inform. Rech. Opérat. 6 (1972) 67-70; Zbl. 236,05105 Zbl0236.05105
- [8] F. Kramer and H. Kramer, On the generalized chromatic number, in: Combinatorics '84, Proc. Int. Conf. Finite Geom. Comb. Struct., Bari/Italy, 1984 (Ann. Discrete Math. 30, 1986) 275-284; Zbl. 601,05020.
- [9] F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes (North-Holland, Amsterdam et al., 1981).
- [10] C.E. Shannon, A theorem on coloring the lines of a network, J. Math. Phys. 28 (1949) 148-151. Zbl0032.43203
- [11] E. Sidorowicz and Z. Skupień, A joint article in preparation.
- [12] Z. Skupień, Some maximum multigraphs and chromatic d-index, in: U. Faigle and C. Hoede, eds., 3rd Twente Workshop on Graphs and Combinatorial Optimization (Fac. Appl. Math. Univ. Twente, Enschede, 1993) 173-175.
- [13] V.G. Vizing, Chromatic class of a multigraph [Russian], Kibernetika 3 (1965) 29-39.
- [14] S. Wagon, (Note) A bound on the chromatic number of graphs without certain induced subgraphs, J. Combin. Theory (B) 29 (1978) 345-346, doi: 10.1016/0095-8956(80)90093-3.

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