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Petr Hliněný, Twin-width is linear in the poset width

August 18 Wednesday @ 5:00 PM - 6:00 PM KST

Zoom ID: 934 3222 0374 (ibsdimag)

Twin-width is a new parameter informally measuring how diverse are the neighbourhoods of the graph vertices, and it extends also to other binary relational structures, e.g. to digraphs and posets. It was introduced quite recently, in 2020 by Bonnet, Kim, Thomassé, and Watrigant. One of the core results of these authors is that FO model checking on graph classes of bounded twin-width is in FPT. With that result, they also claimed that posets of bounded width have bounded twin-width, thus capturing a prior result on FO model checking of posets of bounded width in FPT. However, their translation from poset width to twin-width was indirect and giving only a very loose double-exponential bound.

We prove that posets of width d have twin-width at most 9d with a direct and elementary argument, and show that this bound is tight up to a constant factor. Specifically, for posets of width 2, we prove that in the worst case their twin-width is also equal to 2. These two theoretical results are complemented with straightforward algorithms to construct the respective contraction sequence for a given poset.

(Joint work with my student Jakub Balaban who obtained the main ideas in his bachelor thesis.)

Details

Date:
August 18 Wednesday
Time:
5:00 PM - 6:00 PM KST
Event Category:
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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
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