References
- Calcut, J., Metcalf-Burton, J. (2016). Double branched covers of theta-curves. J. Knot Theory Ramif. 25(8): 1–9.
- Clark, B. (1980). The Heegaard genus of manifolds obtained by surgery on links and knots. Int. J. Math. Math. Sci. 3(3): 583–589. DOI: 10.1155/S0161171280000440.
- Cromwell, P. (2005). Knots and Links. Cambridge: Cambridge Univ. Press.
- Gordon, C., Reid, A. (1995). Tangle decompositions of tunnel number one knots and links. J. Knot Theory Ramif. 4(3): 389–409. DOI: 10.1142/S0218216595000193.
- Heard, D., Hodgson, C., Martelli, B., Petronio, C. (2010). Hyperbolic graphs of small complexity. Experiment. Math. 19(2): 211–236. DOI: 10.1080/10586458.2010.10129072.
- Kinoshita, S. (1973). On elementary ideals of θ-curves in the 3-sphere and 2-links in the 4-sphere. Pacific J. Math. 49: 127–134. DOI: 10.2140/pjm.1973.49.127.
- Kobayashi, T. (1994). A construction of arbitrarily high degeneration of tunnel numbers of knots under connected sum. J. Knot Theory Ramif. 3(2): 179–186. DOI: 10.1142/S0218216594000137.
- Litherland, R. (1989). The Alexander module of a knotted theta-curve. Math. Proc. Cambridge Philos. Soc. 106(1): 95–106. DOI: 10.1017/S0305004100068018.
- Livingston, C. (1995). Knotted symmetric graphs. Proc. Amer. Math. Soc. 123(3): 963–967. DOI: 10.1090/S0002-9939-1995-1273507-3.
- McAtee, J., Silver, D., Williams, S. (2001). Coloring spatial graphs. J. Knot Theory Ramif. 10(1): 109–120. DOI: 10.1142/S0218216501000755.
- Morimoto, K. (1995). There are knots whose tunnel numbers go down under connected sum. Proc. Amer. Math. Soc. 123(11): 3527–3532. DOI: 10.1090/S0002-9939-1995-1317043-4.
- Morimoto, K. (1997). Planar surfaces in a handlebody and a theorem of Gordon-Reid. In: Suzuki, S., ed. KNOTS ’96 (Tokyo). River Edge, NJ: World Sci. Publ., pp. 123–146.
- Norwood, F. (1982). Every two-generator knot is prime. Proc. Amer. Math. Soc. 86(1): 143–147. DOI: 10.1090/S0002-9939-1982-0663884-7.
- Ozawa, M. (2008). Morse position of knots and closed incompressible surfaces. J. Knot Theory Ramif. 17(4): 377–397. DOI: 10.1142/S021821650800618X.
- Ozawa, M. (2012). Bridge position and the representativity of spatial graphs. Topol. Appl. 159(4): 936–947. DOI: 10.1016/j.topol.2011.11.026.
- Scharlemann, M. (1992). Some pictorial remarks on Suzuki’s Brunnian graph. In: Apanasov, B., Neumann, W., Reid, A., Siebenmann, L., eds. Topology ’90. Columbus, OH: deGruyter, pp. 351–354.
- Scharlemann, M. (1984). Tunnel number one knots satisfy the Poenaru conjecture. Topol. Appl. 18(2-3): 235–258. DOI: 10.1016/0166-8641(84)90013-0.
- Scharlemann, M., Schultens, J. (1999). The tunnel number of the sum of n knots is at least n. Topology. 38(2): 265–270. DOI: 10.1016/S0040-9383(98)00002-0.
- Schubert, H. (1954). Über eine numerische Knoteninvariante. Math. Z. 61(1): 245–288. DOI: 10.1007/BF01181346.
- Schultens, J. (2003). Additivity of bridge numbers of knots. Math. Proc. Cambridge Philos. Soc. 135(3): 539–544. DOI: 10.1017/S0305004103006832.
- Simon, J., Wolcott, K. (1990). Minimally knotted graphs in S3. Topol. Appl. 37(2): 163–180. DOI: 10.1016/0166-8641(90)90061-6.
- Suzuki, S. (1984). Almost unknotted θn-curves in the 3-sphere. Kobe J. Math. 1(1): 19–22.
- Taylor, S., Tomova, M. (2018). Additive invariants for knots, links and graphs in 3-manifolds. Geom. Topol. 22(6): 3235–3286. DOI: 10.2140/gt.2018.22.3235.
- Thurston, W. (1980). Geometry and topology of three-manifolds. library.msri.org/books/gt3m/
- Thurston, W. (1997). Three-dimensional Geometry and Topology, Vol. 1. Levy, S., ed. Princeton Mathematical Series 35. Princeton, NJ: Princeton Univ. Press.
- Wolcott, K. (1987). The knotting of theta curves and other graphs in S3. In: McCrory, C., Shifrin, T., eds. Geometry and Topology. New York: Dekker, pp. 325–346.
- Wu, Y. (1996). The classification of nonsimple algebraic tangles. Math. Ann. 304(3): 457–480. DOI: 10.1007/BF01446301.