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Sebastian Siebertz, Rank-width meets stability

September 10 Thursday @ 5:10 PM - 6:10 PM KST

Zoom ID: 934 3222 0374 (ibsdimag)

Forbidden graph characterizations provide a convenient way of specifying graph classes, which often exhibit a rich combinatorial and algorithmic theory. A prime example in graph theory are classes of bounded tree-width, which are characterized as those classes that exclude some planar graph as a minor. Similarly, in model theory, classes of structures are characterized by configurations that are forbidden as logical interpretations or transductions. Two notions from classical model theory are (monadic) stability and (monadic) dependence, which correspond to the impossibility of interpreting with first-order logic (after a vertex coloring step) arbitrary long linear orders and all graphs, respectively.  Examples of monadically stable classes of graphs are nowhere dense graph classes, and examples of monadically dependent classes are classes of bounded rank-width (or equivalently, bounded clique-width), which can be seen as a dense analog of classes of bounded tree-width.

I will give an overview over recent approaches to combine model theoretic and graph theoretic tools to derive structural and algorithmic results for classes of (finite) graphs. I assume no background from logic.

Details

Date:
September 10 Thursday
Time:
5:10 PM - 6:10 PM KST
Event Category:
Event Tags:

Venue

Zoom ID: 934 3222 0374 (ibsdimag)

Organizer

O-joung Kwon (권오정)
IBS 이산수학그룹 Discrete Mathematics Group
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, Fax: +82-42-878-9209
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