学术报告

Proof of the Goldberg-Seymour Conjecture on Edge-Colorings of Multigraphs

发布人：发布时间： 2019-10-21

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**题目：**Proof of the Goldberg-Seymour Conjecture on Edge-Colorings of Multigraphs

**报告人：**臧文安 教授 （香港大学）

**时间：**2019年10月27日 上午9:30-10:30

**地点：**蒙民伟楼1105室

**摘要：**Let G = (V, E) be a multigraph. The chromatic index χ(G) of G is the least integer k for which there is a coloring of E with k colors such that each vertex of G is incident with at most one edge of each color. Let ∆(G) be the maximum degree of G and let Γ(G) be the density of G, defined by Γ(G) = max {2|E(U)| |U| − 1 : U ⊆ V, |U| ≥ 3 and odd} , where E(U) is the set of all edges of G with both ends in U. Clearly, χ ′ (G) ≥ max{∆(G), Γ(G)}. In the 1970s Goldberg and Seymour independently conjectured that χ ′ (G) ≤ max{∆(G) + 1, ⌈Γ(G)⌉}. In this talk I shall present a proof of this conjecture. (Joint work with Guantao Chen and Guangming Jing)

Γ(G) = max {2|E(U)| |U| − 1 : U ⊆ V, |U| ≥ 3 and odd} ,

where E(U) is the set of all edges of G with both ends in U. Clearly, χ ′ (G) ≥ max{∆(G), Γ(G)}. In the 1970s Goldberg and Seymour independently conjectured that χ ′ (G) ≤ max{∆(G) + 1, ⌈Γ(G)⌉}. In this talk I shall present a proof of this conjecture. (Joint work with Guantao Chen and Guangming Jing)

**邀请人：** 赵秋兰 老师