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. 圖論導論，第二版 Englewood Cliffs, NJ: Prentice-Hall, 2000.
可以透過對圖 
重複進行邊刪除和/或邊收縮操作得到，則稱圖 
是圖 
的次要圖。
或完全二分圖 
作為次要圖。此外，Tutte 猜想（1967；West 2000，第 304 頁）並由 Robertson 等人證明，任何 snark 圖都以 Petersen 圖作為次要圖。
，可以在多項式時間內測試 
是否是給定圖 
的次要圖。因此，如果存在停用次要圖的特徵描述，那麼任何透過刪除和收縮操作保持不變的圖屬性都可以在多項式時間內被識別（Fellows 和 Langston 1988，Robertson 和 Seymour 1995）。
的圖擴充套件同構於圖 
的子圖，則稱圖 