浙江师范大学学报（自然科学版）
浙江師範大學學報（自然科學版）
절강사범대학학보（자연과학판）
JOURNAL OF ZHEJIANG NORMAL UNIVERSITY(NATURAL SCIENCES)
2014年
4期
407-411
,共5页
外平面图%无圈边色数%最大度%充分条件
外平麵圖%無圈邊色數%最大度%充分條件
외평면도%무권변색수%최대도%충분조건
outerplane graph%acyclic chromatic index%maximum degree%sufficient condition
一个图G的无圈边染色是一个正常的边染色，使得任一个圈上至少有3种不同的颜色．G的无圈边色数a′（ G）是使得G有无圈k-边染色的最小整数k．设G是一个最大度为4的外平面图．对于现有结果4≤a′（ G）≤5中，何时为4，何时为5，还没有一个完整的刻画．给出一个使得a′（ G）＝4的充分条件，拓展了该领域的相关结果．
一箇圖G的無圈邊染色是一箇正常的邊染色，使得任一箇圈上至少有3種不同的顏色．G的無圈邊色數a′（ G）是使得G有無圈k-邊染色的最小整數k．設G是一箇最大度為4的外平麵圖．對于現有結果4≤a′（ G）≤5中，何時為4，何時為5，還沒有一箇完整的刻畫．給齣一箇使得a′（ G）＝4的充分條件，拓展瞭該領域的相關結果．
일개도G적무권변염색시일개정상적변염색，사득임일개권상지소유3충불동적안색．G적무권변색수a′（ G）시사득G유무권k-변염색적최소정수k．설G시일개최대도위4적외평면도．대우현유결과4≤a′（ G）≤5중，하시위4，하시위5，환몰유일개완정적각화．급출일개사득a′（ G）＝4적충분조건，탁전료해영역적상관결과．
An acyclic edge coloring of a graph G was named as a proper edge coloring such that there would be no bichromatic cycles produced.The acyclic chromatic index a′( G) of G was introduced as the smallest inte-ger k such that G had an acyclic edge coloring by k colors.It was showed that every outerplanar graph G withΔ=4 satisfied 4≤a′( G)≤5, but there was not a fine characterization yet for such outerplanar graph G to have a′(G)=4 or a′(G)=5.A sufficient condition for an outerplanar graph G withΔ=4 to have the acyclic chromatic index 4 was presented.
