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Jean-Florent Raymond, Long induced paths in minor-closed graph classes and beyond

March 30 Wednesday @ 4:30 PM - 5:30 PM KST

Zoom ID: 869 4632 6610 (ibsdimag)

Speaker

In 1982 Galvin, Rival, and Sands proved that in $K_{t,t}$-subgraph free graphs (t being fixed), the existence of a path of order n guarantees the existence of an induced path of order f(n), for some (slowly) increasing function f. The problem of obtaining good lower-bounds for f for specific graph classes was investigated decades later and logarithmic bounds have been obtained for planar graphs (more generally for graphs of bounded genus) and for interval graphs.

In this talk I will show that every graph of pathwidth less than k that has a path of order n also has an induced path of order $Ω(n^{1/k})$. I will then explain how this result can be used to prove the two following generalizations:

  • every graph of treewidth less than k that has a path of order n contains an induced path of order $Ω((\log n)^{1/k})$;
  • for every non-trivial graph class that is closed under topological minors there is a constant d∈(0,1) such that every graph from this class that has a path of order n contains an induced path of order $Ω((\log n)^d)$.

Joint work with Claire Hilaire.

Details

Date:
March 30 Wednesday
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:

Venue

Zoom ID: 869 4632 6610 (ibsdimag)

Organizer

Sang-il Oum (엄상일)
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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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