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    Article

    \(\Gamma \) -Graphic Delta-Matroids and Their Applications

    For an abelian group \(\Gamma \) Γ , a

    Donggyu Kim, Duksang Lee, Sang-il Oum in Combinatorica (2023)

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    Article

    Tangle-Tree Duality: In Graphs, Matroids and Beyond

    We apply a recent tangle-tree duality theorem in abstract separation systems to derive tangle-tree-type duality theorems for width-parameters in graphs and matroids.We further derive a duality theorem for the ...

    Reinhard Diestel, Sang-il Oum in Combinatorica (2019)

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    Article

    Defective Colouring of Graphs Excluding A Subgraph or Minor

    Archdeacon (1987) proved that graphs embeddable on a fixed surface can be 3-coloured so that each colour class induces a subgraph of bounded maximum degree. Edwards, Kang, Kim, Oum and Seymour (2015) proved th...

    Patrice Ossona De Mendez, Sang-Il Oum, David R. Wood in Combinatorica (2019)

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    Article

    A Remark on the Paper “Properties of Intersecting Families of Ordered Sets” by O. Einstein

    O. Einstein (2008) proved Bollobás-type theorems on intersecting families of ordered sets of finite sets and subspaces. Unfortunately, we report that the proof of a theorem on ordered sets of subspaces had a m...

    Sang-Il Oum, Sounggun Wee in Combinatorica (2018)

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    Article

    Finding minimum clique capacity

    Let C be a clique of a graph G. The capacity of C is defined to be (|V (G)\C|+|D|)/2, where D is the set of vertices in V (G)\C that have both a neighbour and a non-neighbour in C. We give a polynomial-time algor...

    Maria Chudnovsky, Sang-Il Oum, Paul Seymour in Combinatorica (2012)