Abstract
Among some results, we prove the following two theorems. (i) Let G be a connected claw-free graph. We arbitrarily color every vertex of G red or blue so that the number of red vertices is even. Then G has vertex-disjoint paths whose end-vertices are exactly the same as the red vertices of G. (ii) Let G be a 3-edge connected claw-free cubic graph. We arbitrarily color every vertex of G red or blue so that the number of red vertices is even and the distance between any two red vertices is at least 3. Then G has a factor F such that \(\deg _F(x) =1\) for every red vertex x and \(\deg _F(y)=2\) for every blue vertex y.
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This study was funded by Japan Society for the Promotion of Science (Grant Nos. 18K13449 and 19K03597).
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Furuya, M., Kano, M. Factors with Red–Blue Coloring of Claw-Free Graphs and Cubic Graphs. Graphs and Combinatorics 39, 85 (2023). https://doi.org/10.1007/s00373-023-02680-6
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DOI: https://doi.org/10.1007/s00373-023-02680-6