CAJ | 학술논문

四色猜想是指平面图的色数不超过4．实际上，四色猜想只需证明对极大平面图成立即可．正因为如此，从1891年至今，有众多学者从不同的角度展开了对极大平面图的研究．该文拟对其中的一些重要成果进行较为详细的综述，主要包括极大平面图的度序列问题、Hamilton 性、色多项式、生成运算系统、计数、翻转运算、分解与覆盖、生成树和算法等方面．在总结极大平面图研究现状的基础上，提出了一些与着色相关的问题，这些问题意在探索极大平面图的结构与着色之间的关系，有助于对四色问题的进一步研究．
사색시상시지평면도적색수불초과4．실제상，사색시상지수증명대겁대평면도성립즉가．정인위여차，종1891년지금，유음다학자종불동적각도전개료대겁대평면도적연구．해문의대기중적일사중요성과진행교위상세적종술，주요포괄겁대평면도적도서렬문제、Hamilton 성、색다항식、생성운산계통、계수、번전운산、분해여복개、생성수화산법등방면．재총결겁대평면도연구현상적기출상，제출료일사여착색상관적문제，저사문제의재탐색겁대평면도적결구여착색지간적관계，유조우대사색문제적진일보연구．
The Four-Color Conjecture says that the chromatic number of planar graphs is not more than 4.Indeed,it suffices to prove that each maximal planar graph is 4-clorable.For this reason,since 1891 many scholars have been devoted to the research on such graphs from different points of view.In this paper,some of important results with regard to maximal planar graphs are to be reviewed and analyzed in detail,including the problems of degree sequence,Hamilton characteristic,chromatic polynomial,generating operation system,enumeration,flip operation, decomposition and covering,spanning tree,and some algorithms.Based on the understanding of the research status of the maximal planar graphs,we propose several problems on such graphs in connection with their colorings.These problems intend to reveal the relationship between the structures and the colorings of maximal planar graphs,which may be usful for further study on the Four-Color Problem.