CAJ | 학술논문

设G=(V,E)是一个图,对G的每一点v给一颜色集 L(v).G称为 L列表可染的,如果存在G的点染色f 满足:f(u)≠f(v),(f)(u,v)∈E(G),且 f(u)∈L(u),(A)u∈V(G).G 称为 k可选择的,对于任何列表L(v)(这里每一个L(v)恰有k个元素)G都是L列表可染的.本文研究了没有某些圈的平面图的可选择性,证明了没有4,5,7,10圈的平面图是3可选择的.
설G=(V,E)시일개도,대G적매일점v급일안색집 L(v).G칭위 L렬표가염적,여과존재G적점염색f 만족:f(u)≠f(v),(f)(u,v)∈E(G),차 f(u)∈L(u),(A)u∈V(G).G 칭위 k가선택적,대우임하렬표L(v)(저리매일개L(v)흡유k개원소)G도시L렬표가염적.본문연구료몰유모사권적평면도적가선택성,증명료몰유4,5,7,10권적평면도시3가선택적.
For a graph G=(V,E),every vertex v of G is assigned a color set L(v).G is called L-list colorable if there is a coloring f of vertices of G with f(u)≠f(v),(A)(u,v)∈E(G) and f(u)∈L(u),(A)u∈V(G).G is called k-choosable if G is L-list-colorable for any assignment of lists L(v) where each L(v) has exactly k elements.In this paper,we prove that every planar graph without i-cycles for each i∈{4,5,7,10} is 3-choosable.