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    "author": [
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          "alternateName": "Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan", 
          "id": "http://www.grid.ac/institutes/grid.19188.39", 
          "name": [
            "Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan"
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        "familyName": "Kuo", 
        "givenName": "Ching-Chen", 
        "type": "Person"
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      {
        "affiliation": {
          "alternateName": "Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan", 
          "id": "http://www.grid.ac/institutes/grid.19188.39", 
          "name": [
            "Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan"
          ], 
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        "familyName": "Lu", 
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    "description": "Let G be an n-node graph with maximum degree \u0394. The Glauber dynamics for G, defined by Jerrum, is a Markov chain over the k-colorings of G. Many classes of G on which the Glauber dynamics mixes rapidly have been identified. Recent research efforts focus on the important case that \u0394\u2009\u2265\u2009dlog2n holds for some sufficiently large constant d. We add the following new results along this direction, where \u03b5 can be any constant with 0\u2009<\u2009\u03b5\u2009<\u20091. \nLet \u03b1\u2009\u2248\u20091.645 be the root of (1\u2009\u2212\u2009e\u2212\u20091/x)2\u2009+\u20092xe\u2212\u20091/x\u2009=\u20092. If G is regular and bipartite and k\u2009\u2265\u2009(\u03b1\u2009+\u2009\u03b5)\u0394, then the mixing time of the Glauber dynamics for G is O(nlogn).Let \u03b2\u2009\u2248\u20091.763 be the root of x\u2009=\u2009e1/x. If the number of common neighbors for any two adjacent nodes of G is at most \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$\\frac{\\epsilon^{1.5}\\Delta}{360e}$\\end{document} and k\u2009\u2265\u2009(1\u2009+\u2009\u03b5)\u03b2\u0394, then the mixing time of the Glauber dynamics is O(nlogn).", 
    "editor": [
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        "familyName": "Chao", 
        "givenName": "Kun-Mao", 
        "type": "Person"
      }, 
      {
        "familyName": "Hsu", 
        "givenName": "Tsan-sheng", 
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        "givenName": "Der-Tsai", 
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      }
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      "name": "Algorithms and Computation", 
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      "Glauber dynamics", 
      "maximum degree \u0394.", 
      "degree \u0394.", 
      "Markov chain", 
      "important case", 
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      "regular bipartite graphs", 
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      "efforts", 
      "cases", 
      "results", 
      "roots"
    ], 
    "name": "Randomly Coloring Regular Bipartite Graphs and Graphs with Bounded Common Neighbors", 
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