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  1. No Access

    Article

    Generalized List Colouring of Graphs

    This paper disproves a conjecture in Wang et al. (Graphs Comb. 31:1779–1787, 2015) and answers in the negative a question in Dvořák et al. (Electron J Comb:P26, 2019). In return, we pose five open problems.

    Eun-Kyung Cho, Ilkyoo Choi, Yiting Jiang, Ringi Kim, Boram Park… in Graphs and Combinatorics (2021)

  2. No Access

    Article

    Degeneracy and Colorings of Squares of Planar Graphs without 4-Cycles

    We prove several results on coloring squares of planar graphs without 4-cycles. First, we show that if G is such a graph, then G2 is (Δ(G) + 72)-degenerate. This implies an upper bound of Δ(G) ∣ 73 on the chromat...

    Ilkyoo Choi, Daniel W. Cranston, Théo Pierron in Combinatorica (2020)

  3. No Access

    Article

    Largest 2-Regular Subgraphs in 3-Regular Graphs

    For a graph G, let \(f_2(G)\) ...

    Ilkyoo Choi, Ringi Kim, Alexandr V. Kostochka, Boram Park… in Graphs and Combinatorics (2019)

  4. No Access

    Article

    On operations preserving semi-transitive orientability of graphs

    We consider the class of semi-transitively orientable graphs, which is a much larger class of graphs compared to transitively orientable graphs, in other words, comparability graphs. Ever since the concept of ...

    Ilkyoo Choi, **ha Kim, Minki Kim in Journal of Combinatorial Optimization (2019)

  5. No Access

    Chapter and Conference Paper

    3-Coloring Triangle-Free Planar Graphs with a Precolored 9-Cycle

    Given a triangle-free planar graph G and a cycle C of length 9 in G, we characterize all situations where a 3-coloring of C does not extend to a proper 3-coloring of G. This extends previous results for the lengt...

    Ilkyoo Choi, Jan Ekstein, Přemysl Holub, Bernard Lidický in Combinatorial Algorithms (2015)