A cover of a graph G is a graph H with vertex set V(H)=∪_(v∈V(G))L_(v),where L_(v)={v}×[s],and the edge set M=∪_(uv∈E(G))M_(uv),where Muv is a matching between L_(u) and L_(v).A vertex set T⊆V(H)is a transver...A cover of a graph G is a graph H with vertex set V(H)=∪_(v∈V(G))L_(v),where L_(v)={v}×[s],and the edge set M=∪_(uv∈E(G))M_(uv),where Muv is a matching between L_(u) and L_(v).A vertex set T⊆V(H)is a transversal of H if∣T∩Lv∣=1 for each v∈V(G).Let f be a nonnegative integer valued function on the vertex-set of H.If for any nonempty subgraphΓof H[T],there exists a vertex x∈V(H)such that d(x)<f(x),then T is called a strictly f-degenerate transversal.In this paper,we give a sufficient condition for the existence of strictly f-degenerate transversal for planar graphs without chorded 6-cycles.As a consequence,every planar graph without subgraphs isomorphic to the configurations is DP-4-colorable.展开更多
基金supported by NSFC(Grant Nos.12171436 and 12371360)supported by NSFC(Grant No.12031018)NSFSD(Grant No.ZR2022MA060)。
文摘A cover of a graph G is a graph H with vertex set V(H)=∪_(v∈V(G))L_(v),where L_(v)={v}×[s],and the edge set M=∪_(uv∈E(G))M_(uv),where Muv is a matching between L_(u) and L_(v).A vertex set T⊆V(H)is a transversal of H if∣T∩Lv∣=1 for each v∈V(G).Let f be a nonnegative integer valued function on the vertex-set of H.If for any nonempty subgraphΓof H[T],there exists a vertex x∈V(H)such that d(x)<f(x),then T is called a strictly f-degenerate transversal.In this paper,we give a sufficient condition for the existence of strictly f-degenerate transversal for planar graphs without chorded 6-cycles.As a consequence,every planar graph without subgraphs isomorphic to the configurations is DP-4-colorable.
