, Volume 36, Issue 1-2, pp 367-372

A note on edge-choosability of planar graphs without intersecting 4-cycles

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Abstract

A graph G is edge-L-colorable, if for a given edge assignment L={L(e):eE(G)}, there exits a proper edge-coloring φ of G such that φ(e)∈L(e) for all eE(G). If G is edge-L-colorable for every edge assignment L with |L(e)|≥k for eE(G), then G is said to be edge-k-choosable. In this paper, We investigate structural of planar graphs without intersecting 4-cycles and show that every planar graph without intersecting 4-cycles is edge-k-choosable, where $k=\max\{7,\Delta(G)+1\}$ .

This work was supported by the Nature Science Foundation of Shandong Province (Y2008A20), also was supported by the Scientific Research and Development Project of Shandong Provincial Education Department (TJY0706) and the Science and Technology Foundation of University of Jinan (XKY0705).