Demaine, E. D.; Hajiaghayi, M.; and Kawarabayashi, K.-I. "Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring." In Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2005), Pittsburgh, PA, October 23-25, 2005. pp. 637-646.Demaine, E. D.; Hajiaghayi, M.; and Kawarabayashi, K.-I. "Algorithmic Graph Minor Theory: Improved Grid Minor Bounds and Wagner's Contraction." In Algorithms and Computation. Proceedings of the 17th International Symposium (ISAAC 2006) held in Kolkata, December 18-20, 2006 (Ed. T. Asano). Berlin: Springer, pp. 3-15, 2006.Fellows, M. R. and Langston, M. A. "Nonconstructive Tools for Proving Polynomial-Time Decidability." J. ACM35, 727-739, 1988.Mohar, B. and Škoda, P. "Excluded Minors for the Klein Bottle I. Low Connectivity Case." 1 Feb 2020. https://arxiv.org/abs/2002.00258.Robertson, N.; Sanders, D. P.; Seymour, P. D.; and Thomas, R. "A New Proof of the Four Colour Theorem." Electron. Res. Announc. Amer. Math. Soc.2, 17-25, 1996.Robertson, N.; Sanders, D. P.; and Thomas, R. "The Four-Color Theorem." http://www.math.gatech.edu/~thomas/FC/fourcolor.html.Robertson, N. and Seymour, P. D. "Graph Minors. XIII. The Disjoint Paths Problem." J. Combin. Th., Ser. B63, 65-110, 1995.Tutte, W. T. "A geometrical Version of the Four Color Problem." In Combinatorial Math. and Its Applications (Ed. R. C. Bose and T. A. Dowling). Chapel Hill, NC: University of North Carolina Press, 1967.West, D. B. 图论导论，第二版 Englewood Cliffs, NJ: Prentice-Hall, 2000.
可以通过对图 
重复进行边删除和/或边收缩操作得到，则称图 
是图 
的次要图。
或完全二分图 
作为次要图。此外，Tutte 猜想（1967；West 2000，第 304 页）并由 Robertson 等人证明，任何 snark 图都以 Petersen 图作为次要图。
，可以在多项式时间内测试 
是否是给定图 
的次要图。因此，如果存在禁用次要图的特征描述，那么任何通过删除和收缩操作保持不变的图属性都可以在多项式时间内被识别（Fellows 和 Langston 1988，Robertson 和 Seymour 1995）。
的图扩展同构于图 
的子图，则称图 