五邑大学学报：自然科学版
五邑大學學報：自然科學版
오읍대학학보：자연과학판
Journal of Wuyi University(Natural Science Edition)
2012年
2期
15-17
,共3页
无向图%色数%着色数%围长
無嚮圖%色數%著色數%圍長
무향도%색수%착색수%위장
undirected graph%chromatic number%coloring number%girth
证明了对于围长不少于2k1的图G,其色数X（G）≤c（（bk,2k＋1＋2）n）1/k＋1＋2,其中c=c（k）且limk→∞ c（k）=1,bt,k是G的booksize.另外还证明了对于围长不少于2k＋1的图G,其着色数σ（G）≤[bk,2k＋1＋1）n/2]1/k＋2.
證明瞭對于圍長不少于2k1的圖G,其色數X（G）≤c（（bk,2k＋1＋2）n）1/k＋1＋2,其中c=c（k）且limk→∞ c（k）=1,bt,k是G的booksize.另外還證明瞭對于圍長不少于2k＋1的圖G,其著色數σ（G）≤[bk,2k＋1＋1）n/2]1/k＋2.
증명료대우위장불소우2k1적도G,기색수X（G）≤c（（bk,2k＋1＋2）n）1/k＋1＋2,기중c=c（k）차limk→∞ c（k）=1,bt,k시G적booksize.령외환증명료대우위장불소우2k＋1적도G,기착색수σ（G）≤[bk,2k＋1＋1）n/2]1/k＋2.
In this paper, it is proved that for graph G whose coloring number is X（G）≤c（（bk,2k＋1＋2）n）1/k＋1＋2 where c=c（k）with limk→∞ c（k）=1and whose girth is at least 2k＋1, bl.k is the booksize of G. It is also proved that the coloring number for graph G with girth at least 2k ＋1 is σ（G）≤[bk,2k＋1＋1）n/2]1/k＋2.
