CAJ | 학술논문

混合超图的上、下色数的研究是超图研究中一个重要的话题.由于超图本身结构上的复杂性,近年来对超图色性的研究也近局限于对一些特殊图类的研究,其中完全一致混合超图是最为热门的图类之一.给出了D完全（C不完全）一致混合超图的概念,并运用组合数学中有关分划的思想和方法对该图类的色性进行了进一步的研究,对相关文献中给出的结论进行了推广,得到了一个较为一般化的结论.并在该定理的证明中得到并证明了一个关于混合超图C稳定集的重要论断,对超图色性研究有着重要的意义.
혼합초도적상、하색수적연구시초도연구중일개중요적화제.유우초도본신결구상적복잡성,근년래대초도색성적연구야근국한우대일사특수도류적연구,기중완전일치혼합초도시최위열문적도류지일.급출료D완전（C불완전）일치혼합초도적개념,병운용조합수학중유관분화적사상화방법대해도류적색성진행료진일보적연구,대상관문헌중급출적결론진행료추엄,득도료일개교위일반화적결론.병재해정리적증명중득도병증명료일개관우혼합초도C은정집적중요론단,대초도색성연구유착중요적의의.
It is a important topic to study the upper and lower chromatical number of the mixed hypergraphs. As the hypergraphs have a complex structure, all study on chromatical properties of the hypergraphs are limited to only some special kind of hypergraphs. The complete uniform mixed hypergraph is the most popular one among they. In this artical, a new concept that the ：D-complete uniform mixed hypergraph was given~ and further studied its the upper chromatical number on previously a initial result basis, and a general result was attained. In the course of proving this conclusion, we find and prove a important predication connection with the stable set of the mixed hyper~raphs, which has a important mean.