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DTSTART;TZID=Asia/Seoul:20190128T160000
DTEND;TZID=Asia/Seoul:20190128T170000
DTSTAMP:20260423T160000
CREATED:20190102T015548Z
LAST-MODIFIED:20240705T211438Z
UID:348-1548691200-1548694800@dimag.ibs.re.kr
SUMMARY:Seog-Jin Kim (김석진)\, Signed colouring and list colouring of  k-chromatic graphs
DESCRIPTION: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. \nLet 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.
URL:https://dimag.ibs.re.kr/event/2019-01-28/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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