%0 Generic %1 cowen2021integrated %A Cowen, Robert %D 2021 %K combinatorics maxcut %T Integrated Neighborhood Colorings of Graphs %U http://arxiv.org/abs/2112.07709 %X The idea that those different from you are ünfriendly" is captured in the definition of unfriendly 2-colorings in graph theory in a paper by Aharoni, Milner and Prikry, where they prove that every finite graph has an unfriendly coloring. We give a more general definition for all n>1, that we call "integrated" rather than ünfriendly." Then we prove that every finite graph has an integrated n-coloring, n>1. We then give some applications to various graph coloring problems and to some max-cut problems.

@misc{cowen2021integrated, abstract = {The idea that those different from you are "unfriendly" is captured in the definition of unfriendly 2-colorings in graph theory in a paper by Aharoni, Milner and Prikry, where they prove that every finite graph has an unfriendly coloring. We give a more general definition for all n>1, that we call "integrated" rather than "unfriendly." Then we prove that every finite graph has an integrated n-coloring, n>1. We then give some applications to various graph coloring problems and to some max-cut problems.}, added-at = {2022-02-14T09:12:30.000+0100}, author = {Cowen, Robert}, biburl = {https://www.bibsonomy.org/bibtex/29a8b5696c360558b6faba2edff418c9f/iliyasnoman}, description = {Integrated Neighborhood Colorings of Graphs}, interhash = {a4f41ba0614e737a94198acbb3dd581c}, intrahash = {9a8b5696c360558b6faba2edff418c9f}, keywords = {combinatorics maxcut}, note = {cite arxiv:2112.07709}, timestamp = {2022-02-14T09:12:30.000+0100}, title = {Integrated Neighborhood Colorings of Graphs}, url = {http://arxiv.org/abs/2112.07709}, year = 2021 }