Abstract
In this paper some new results on edge coloring of graphs are introduced. This paper deals mainly with edge cover coloring, g-edge cover coloring, (g, f)-coloring and equitable edge coloring. Some new problems and conjectures are presented.
This research was supported by NNSF(10471078)and RSDP(20040422004) of China.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Balister, P.N., Riordan, O.M., Schelp, R.H.: Vertex Distinguishing Edge Colorings of Graphs. J. Graph Theory 42, 95–109 (2003)
Gupta, R.P.: On Decompositions of a Multigraph into Spanning Subgraphs. Bull. Amer. Math. Soc. 80, 500–502 (1974)
Hakimi, S.L., Kariv, O.: A Generalization of Edge-Coloring in Graphs. J. Graph Theory 10, 139–154 (1986)
Hilton, A.J., de Werra, D.: A Sufficient Condition for Equitable Edge-Coloring of Simple Graphs. Discrete Math. 128, 179–201 (1994)
Li, J., Zhang, Z., Chen, X., Sun, Y.: A Note on Adjacent Strong Edge Coloring of K(n, m). Acta Math. Appl. 22(2) (English Series), 283–286 (2006)
Liu, G.: On (g, f)-Factors and Factorizations. Acta Math. Sinica 37, 230–237 (1994)
Liu, G., Deng, X.: A Polynomial Algorithm for Finding (g, f)-Colorings Orthogonal to Stars in Bipartite Graphs. Science in China, Ser. A. 35(3), 334–344 (2005)
Miao, L.: The Edge Cover Coloring of Graphs. Ph.D. Thesis of Shandong University (2000)
Miao, L., Liu, G.: A Edge Cover Coloring and Fractional Edge Cover Coloring. J. of Systems Science and Complexing 15(2), 187–193 (2002)
Nakano, S., Nishizeki, T., Saito, N.: On the f-Coloring of Multigraphs. IEEE Trans. Circuit and Syst. 35(3), 345–353 (1988)
Nakano, S., Nishizeki, T., Saito, N.: On the fg-Coloring of Graphs. Combinatorica 10(1), 67–80 (1990)
Nakano, S., Nishizeki, T.: Scheduling File Transfers under Port and Channel Constraints. Internat. J. Found. Comput. Sci. 4(2), 425–431 (1993)
Song, H., Liu, G.: On f-Edge Cover-Coloring in Multigraphs. Acta Math. Sin. 48(5), 910–919 (2005)
Song, H., Liu, G.: Some Properties of Edge Cover Critical Graphs. Advances in Math. 33, 96–102 (2004)
Song, H., Liu, G.: Applications of an Equitable Edge-Coloring Theorem. The International Conference on Mathematical Programming, pp. 19–22 (2002)
Vizing, V.G.: On an Estimate of the Chromatics Class of a p-Graph (Russian). Diskret. Analiz. 3, 25–30 (1964)
de Werra, D.: Equitable Colorations of Graphs. Rev. Fran?aise Informat. Recherche Oprationnelle R-3, 3–8 (1971)
Xin, Y.: On Edge-Colouring Problems of Graphs. Ph.M. Thesis of Shandong University (2005)
Xu, C.: Some Topics on Edge Coloring Problems. Post-doctor Report of Shandong University (2005)
Xu, C., Liu, G.: The Existence of (g, f)-Coloring. Submitted to the Electronic J. Comb.
Xu, C., Liu, G.: On Super f-Edge Cover-Coloring in Multigraphs. Submitted to Discrete Math.
Xu, C., Liu, G.: A Note on Edge Covered Chromatic Index of Multigraphs. Submitted to Appl. Math. Letters
Xu, C., Liu, G.: Edge Covered Critical Multigraphs. Submitted to Discrete Math.
Xu, C., Liu, G.: On Equitable Edge-Coloring in Multigraphs. Submitted to Science in China, Ser A
Zhang, Z., Liu, L., Wang, J.: Adjacent Strong Edge Coloring of Graphs. Applied Math. Letters 15, 623–626 (2002)
Zhou, X., Fuse, K., Nishizeki, T.: A Linear Algorithm for Finding [g, f]-Colorings of Partial k-Trees. Algorithmica 27, 227–243 (2000)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Liu, G., Xu, C. (2007). Some Topics on Edge-Coloring. In: Akiyama, J., Chen, W.Y.C., Kano, M., Li, X., Yu, Q. (eds) Discrete Geometry, Combinatorics and Graph Theory. CJCDGCGT 2005. Lecture Notes in Computer Science, vol 4381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70666-3_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-70666-3_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70665-6
Online ISBN: 978-3-540-70666-3
eBook Packages: Computer ScienceComputer Science (R0)