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Packing subdivisions into regular graphs.

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Τίτλος: Packing subdivisions into regular graphs.
Συγγραφείς: Montgomery, Richard1 (AUTHOR), Petrova, Kalina2 (AUTHOR), Ranganathan, Arjun3 (AUTHOR), Tan, Jane4 (AUTHOR)
Πηγή: Proceedings of the American Mathematical Society. Sep2026, Vol. 154 Issue 9, p3693-3704. 12p.
Θεματικοί όροι: *Regular graphs, *Subgraphs, *Combinatorics, *Graph theory
Περίληψη: We show that, for any graph F and \eta >0, there exists a d_0=d_0(F,\eta) such that every n-vertex d-regular graph with d \geq d_0 has a collection of vertex-disjoint F-subdivisions covering at least (1-\eta)n vertices. This verifies a conjecture of Verstraëte from 2002 and improves a recent result of Letzter, Methuku and Sudakov which additionally required d to be at least polylogarithmic in n. [ABSTRACT FROM AUTHOR]
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  Data: Packing subdivisions into regular graphs.
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  Data: <searchLink fieldCode="JN" term="%22Proceedings+of+the+American+Mathematical+Society%22">Proceedings of the American Mathematical Society</searchLink>. Sep2026, Vol. 154 Issue 9, p3693-3704. 12p.
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  Data: *<searchLink fieldCode="DE" term="%22Regular+graphs%22">Regular graphs</searchLink><br />*<searchLink fieldCode="DE" term="%22Subgraphs%22">Subgraphs</searchLink><br />*<searchLink fieldCode="DE" term="%22Combinatorics%22">Combinatorics</searchLink><br />*<searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink>
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  Data: We show that, for any graph F and \eta >0, there exists a d_0=d_0(F,\eta) such that every n-vertex d-regular graph with d \geq d_0 has a collection of vertex-disjoint F-subdivisions covering at least (1-\eta)n vertices. This verifies a conjecture of Verstraëte from 2002 and improves a recent result of Letzter, Methuku and Sudakov which additionally required d to be at least polylogarithmic in n. [ABSTRACT FROM AUTHOR]
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        Value: 10.1090/proc/17684
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 12
        StartPage: 3693
    Subjects:
      – SubjectFull: Regular graphs
        Type: general
      – SubjectFull: Subgraphs
        Type: general
      – SubjectFull: Combinatorics
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      – SubjectFull: Graph theory
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      – TitleFull: Packing subdivisions into regular graphs.
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            NameFull: Petrova, Kalina
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            – D: 01
              M: 09
              Text: Sep2026
              Type: published
              Y: 2026
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              Value: 154
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              Value: 9
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            – TitleFull: Proceedings of the American Mathematical Society
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