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# Seog-Jin Kim (김석진), Signed colouring and list colouring of k-chromatic graphs

## Monday, January 28, 2019 @ 4:00 PM - 5:00 PM

Room B232, IBS (기초과학연구원)

### Speaker

Seog-Jin Kim (김석진)
Department of Mathematics Education, Konkuk University
http://home.konkuk.ac.kr/~skim12/

A signed graph is a pair (G, σ), where G is a graph and σ: E(G) → {1,-1} is a signature of G. A set S of integers is symmetric if I∈S implies that -i∈S. A k-colouring of (G,σ) is a mapping f:V(G) → Nk such that for each edge e=uv, f(x)≠σ(e) f(y), where Nk is a symmetric integer set of size k. We define the signed chromatic number of a graph G to be the minimum integer k such that for any signature σ of G, (G, σ) has a k-colouring.

Let f(n,k) be the maximum signed chromatic number of an n-vertex k-chromatic graph. This paper determines the value of f(n,k) for all positive integers n ≥ k. Then we study list colouring of signed graphs. A list assignment L of G is called symmetric if L(v) is a symmetric integer set for each vertex v. The weak signed choice number ch±w(G) of a graph G is defined to be the minimum integer k such that for any symmetric k-list assignment L of G, for any signature σ on G, there is a proper L-colouring of (G, σ). We prove that the difference ch±w(G)-χ±(G) can be arbitrarily large. On the other hand, ch±w(G) is bounded from above by twice the list vertex arboricity of G. Using this result, we prove that ch±w(K2⋆n)= χ±(K2⋆n) = ⌈2n/3⌉ + ⌊2n/3⌋. This is joint work with Ringi Kim and Xuding Zhu.

## Details

Date:
Monday, January 28, 2019
Time:
4:00 PM - 5:00 PM
Event Category:
Event Tags:
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Room B232
IBS (기초과학연구원)

## Organizer

Sang-il Oum (엄상일)
Website:
https://dimag.ibs.re.kr/home/sangil/
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr