2-平面相似图的子染色是NP-完全的
2-subcoloring is NP-complete for planar comparability graphs
摘要：
一个图的$k$ -子染色是将顶点集划分为至多$k$簇图，即没有导出$P_3$的图。2-对于可比较图和平面图的三个子类，即最大度为4的无三角形平面图、最大度为4的平面完美图和围长为5的平面图，子染色是NP-完全的。我们证明了对于最大度为4的平面可比图，2-子染色也是NP-完全的。
英文摘要：
A $k$-subcoloring of a graph is a partition of the vertex set into at most $k$ cluster graphs, that is, graphs with no induced $P_3$. 2-subcoloring is known to be NP-complete for comparability graphs and three subclasses of planar graphs, namely triangle-free planar graphs with maximum degree 4, planar perfect graphs with maximum degree 4, and planar graphs with girth 5. We show that 2-subcoloring is also NP-complete for planar comparability graphs with maximum degree 4.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
