KMS Of Academy of mathematics and systems sciences, CAS
| DENSITIES, MATCHINGS, AND FRACTIONAL EDGE-COLORINGS | |
Chen, Xujin1,2 ; Zang, Wenan3; Zhao, Qiulan4
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| 2019 | |
| Source Publication | SIAM JOURNAL ON OPTIMIZATION
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| ISSN | 1052-6234 |
| Volume | 29Issue:1Pages:240-261 |
| Abstract | Given a multigraph G = (V, E) with a positive rational weight w(e) on each edge e, the weighted density problem (WDP) is to find a subset U of V, with vertical bar U vertical bar >= 3 and odd, that maximizes 2w(U)/(vertical bar U vertical bar - 1), where w(U) is the total weight of all edges with both ends in U, and the weighted fractional edge-coloring problem can be formulated as the following linear program: minimize 1(T) x subject to Ax = w, x >= 0, where A is the edge-matching incidence matrix of G. These two problems are closely related to the celebrated Goldberg-Seymour conjecture on edge-colorings of multigraphs, and are interesting in their own right. Even when w(e) = 1 for all edges e, determining whether WDP can be solved in polynomial time was posed by Jensen and Toft [Topics in Chromatic Graph Theory, Cambridge University Press, Cambridge, 2015, pp. 327-357] and by Stiebitz et al. [Graph Edge Colouring: Vizing's Theorem and Goldberg's Conjecture, John Wiley, New York, 2012] as an open problem. In this paper we present strongly polynomial-time algorithms for solving them exactly, and develop a novel matching removal technique for multigraph edge-coloring. |
| Keyword | multigraph density matching fractional edge-coloring algorithm |
| DOI | 10.1137/17M1147676 |
| Language | 英语 |
| Funding Project | NSF of China[11801266] ; Research Grants Council of Hong Kong ; Fundamental Research Funds for the Central Universities[14380020] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000462593800010 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/34216 |
| Collection | 应用数学研究所 |
| Corresponding Author | Zhao, Qiulan |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Univ Hong Kong, Dept Math, Hong Kong, Peoples R China 4.Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China |
| Recommended Citation GB/T 7714 | Chen, Xujin,Zang, Wenan,Zhao, Qiulan. DENSITIES, MATCHINGS, AND FRACTIONAL EDGE-COLORINGS[J]. SIAM JOURNAL ON OPTIMIZATION,2019,29(1):240-261. |
| APA | Chen, Xujin,Zang, Wenan,&Zhao, Qiulan.(2019).DENSITIES, MATCHINGS, AND FRACTIONAL EDGE-COLORINGS.SIAM JOURNAL ON OPTIMIZATION,29(1),240-261. |
| MLA | Chen, Xujin,et al."DENSITIES, MATCHINGS, AND FRACTIONAL EDGE-COLORINGS".SIAM JOURNAL ON OPTIMIZATION 29.1(2019):240-261. |
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