Three edge-coloring conjectures
Richard H. Schelp
Discussiones Mathematicae Graph Theory, Tome 22 (2002), p. 173-182 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

The focus of this article is on three of the author's open conjectures. The article itself surveys results relating to the conjectures and shows where the conjectures are known to hold.

Publié le : 2002-01-01
EUDML-ID : urn:eudml:doc:270546 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1166,
     author = {Richard H. Schelp},
     title = {Three edge-coloring conjectures},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {22},
     year = {2002},
     pages = {173-182},
     zbl = {1010.05026},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1166}
}

Richard H. Schelp. Three edge-coloring conjectures. Discussiones Mathematicae Graph Theory, Tome 22 (2002) pp. 173-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1166/

[000] [1] M. Aigner, E. Triesch and Zs. Tuza, Irregular assignments and vertex-distinguishing edge-colorings, in: Combinatorics 90, A. Barlotti et al, eds. (Elsevier Science Pub., New York, 1992), 1-9.

[001] [2] P.N. Balister, Packing circuits in Kₙ, Combinatorics, Probability and Computing 10 (2001) 463-499, doi: 10.1017/S0963548301004771. | Zbl 1113.05309

[002] [3] P.N. Balister, B. Bollobás and R.H. Schelp, Vertex-distinguishing colorings of graphs with Δ(G) = 2, (to appear in Discrete Mathematics). | Zbl 1005.05019

[003] [4] P.N. Balister, A. Kostochka, Hao Li and R.H. Schelp, Balanced edge colorings, preprint.

[004] [5] P.N. Balister, O.M. Riordan, R.H. Schelp, Vertex-distinguishing edge colorings of graphs, (to appear in J. Graph Theory). | Zbl 1008.05067

[005] [6] C. Bazgan, A. Harket-Benhamdine, Hao Li and Mariusz Woźniak, On the vertex-distinguishing proper edge-colorings of graphs, J. Combin. Theory (B) 74 (1999) 288-301, doi: 10.1006/jctb.1998.1884. | Zbl 0932.05036

[006] [7] B. Bollobás, A. Kostochka and R.H. Schelp, Local and mean Ramsey numbers for trees, J. Combin. Theory (B) 79 (2000) 100-103, doi: 10.1006/jctb.2000.1950. | Zbl 1028.05068

[007] [8] A.C. Burris, Vertex-distinguishing edge-colorings, Ph.D. Dissertation (Memphis State University, August 1993). | Zbl 0886.05068

[008] [9] A.C. Burris and R.H. Schelp, Vertex-distinguishing proper edge-colorings, J. Graph Theory 26 (2) (1997) 73-82, doi: 10.1002/(SICI)1097-0118(199710)26:2<73::AID-JGT2>3.0.CO;2-C | Zbl 0886.05068

[009] [10] P. Erdős and V.T. Sós, Some Remarks on Ramsey's and Turán's theorems, in: P. Erdoos et al eds., Comb. Theory and Appl., Proc. Colloq. Math. Soc. János Bolyai 4, Balatonfüred, 1969 (North-Holland, Amsterdam, 1970) 395-404.

[010] [11] Y. Caro, On several variations of the Turan and Ramsey numbers, J. Graph Theory 16 (1992) 257-266, doi: 10.1002/jgt.3190160309. | Zbl 0760.05066

[011] [12] Y. Caro and Zs. Tuza, On k-local and k-mean colorings of graphs and hypergraphs, Quart. J. Math. Oxford 44 (2) (1993) 385-398, doi: 10.1093/qmath/44.4.385.

[012] [13] J. Cerńy, M. Hornák and R. Soták, Observability of a graph, Math. Slovaca 46 (1996) 21-31. | Zbl 0853.05040

[013] [14] R.A. Clapsadle, Polychromatic structures and substructures in edge-colorings of graphs, Ph. D. Dissertation (University of Memphis, 1994).

[014] [15] R.A. Clapsadle and R.H. Schelp, Local edge-colorings that are global, J. Graph Theory 18 (1994) 389-399, doi: 10.1002/jgt.3190180409. | Zbl 0813.05027

[015] [16] O. Favaron, Hao Li and R.H. Schelp, Strong edge-colorings of graphs, Discrete Math. 159 (1996) 103-109, doi: 10.1016/0012-365X(95)00102-3. | Zbl 0859.05042

[016] [17] A. Galluccio, M. Simonovits and G. Simonyi, On the structure of co-critical graphs, in: Proc. of Graph Theory, Combinatorics, and Computing (Kalamazoo, MI) 2 (1995) 1053-1071. | Zbl 0843.05041

[017] [18] A. Gyárfás, J. Lehel, R.H. Schelp and Zs. Tuza, Ramsey numbers for local colorings, Graphs and Combinatorics 3 (1987) 267-277, doi: 10.1007/BF01788549. | Zbl 0621.05023

[018] [19] M. Hornák and R. Soták, Observability of complete multipartite graphs with equipotent parts, Ars Combin. 41 (1995) 289-301. | Zbl 0841.05032

[019] [20] M. Hornák and R. Soták, Asymptotic behavior of the observability of Qₙ, preprint. | Zbl 0890.05028

[020] [21] R.H. Schelp, Local and mean k-Ramsey numbers for the complete graph, J. Graph Theory 24 (1997) 201-203, doi: 10.1002/(SICI)1097-0118(199703)24:3<201::AID-JGT1>3.0.CO;2-T | Zbl 0878.05060

[021] [22] M. Truszcznyński, Generalized local colorings of graphs, J. Combin Theory (B) 54 (1992) 178-188, doi: 10.1016/0095-8956(92)90049-4. | Zbl 0769.05041

[022] [23] M. Truszcyński and Zs. Tuza, Linear upper bounds for local Ramsey numbers, Graphs and Combinatorics 3 (1987) 67-73.