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極大平面圖的結(jié)構(gòu)與著色理論 (4)-運算與Kempe等價類

許進

許進. 極大平面圖的結(jié)構(gòu)與著色理論 (4)-運算與Kempe等價類[J]. 電子與信息學報, 2016, 38(7): 1557-1585. doi: 10.11999/JEIT160483
引用本文: 許進. 極大平面圖的結(jié)構(gòu)與著色理論 (4)-運算與Kempe等價類[J]. 電子與信息學報, 2016, 38(7): 1557-1585. doi: 10.11999/JEIT160483
XU Jin. Theory on Structure and Coloring of Maximal Planar Graphs (4)-Operations and Kempe Equivalent Classes[J]. Journal of Electronics & Information Technology, 2016, 38(7): 1557-1585. doi: 10.11999/JEIT160483
Citation: XU Jin. Theory on Structure and Coloring of Maximal Planar Graphs (4)-Operations and Kempe Equivalent Classes[J]. Journal of Electronics & Information Technology, 2016, 38(7): 1557-1585. doi: 10.11999/JEIT160483

極大平面圖的結(jié)構(gòu)與著色理論 (4)-運算與Kempe等價類

doi: 10.11999/JEIT160483
基金項目: 

國家973計劃項目(2013CB329600),國家自然科學基金(61372191, 61472012, 61472433, 61572046, 61502012, 61572492, 61572153, 61402437)

Theory on Structure and Coloring of Maximal Planar Graphs (4)-Operations and Kempe Equivalent Classes

Funds: 

The National 973 Program of China (2013CB329600), The National Natural Science Foundation of China (61372191, 61472012, 61472433, 61572046, 61502012, 61572492, 61572153, 61402437)

  • 摘要: 設G是一個k-色圖,若G的所有k-著色是Kempe等價的,則稱G為Kempe圖。表征色數(shù)3的Kempe圖特征是一尚待解決難題。該文對極大平面圖的Kempe等價性進行了研究,其主要貢獻是:(1)發(fā)現(xiàn)導致兩個4-著色是Kempe等價的關鍵子圖為2-色耳,故對2-色耳的特征進行了深入研究;(2)引入-特征圖,清晰地刻畫了一個圖中所有4-著色之間的關聯(lián)關系,并深入研究了-特征圖的性質(zhì);(3)揭示了4-色非Kempe極大平面圖的Kempe等價類可分為樹型,圈型和循環(huán)圈型,并指出這3種類型可同時存在于一個極大平面圖的4-著色集中;(4)研究了Kempe極大平面圖特征,給出了該類圖的多米諾遞推構(gòu)造法,以及兩個Kempe極大平面圖猜想。
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出版歷程
  • 收稿日期:  2016-05-11
  • 修回日期:  2016-05-30
  • 刊出日期:  2016-07-19

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