边染色图中的正常染色的路和圈

Properly colored paths and cycles in edge colored graphs

讨论了无三角形的边染色图中的正常染色的路和圈,在无三角形图中改进了原有的结果。证明了在顶点的最小色度至少为d(d≥2)的条件下,边染色图G或者存在长至少为4d-2的正常染色的路,或者存在长至少为2「2d/3的正常染色的圈。

Properly colored paths and cycles in edge colored triangle-free graphs are discussed,and the known result is improved in triangle-free graphs.It is proved that in any edge colored triangle-free graph G with color degree at least d（d≥2）,there exists either a properly colored path of size at least 4d-2,or a properly colored cycle of size at least 2「2d/3.