Abstract
There have been several generalizations or extensions of the proper connection number. We discuss a few of these in this chapter.
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References
Bi, Z., Byers, A., Zhang, P.: Proper Hamiltonian-connected graphs. Manuscript
Bi, Z., Chartrand, G., Johns, G., Zhang, P.: On minimum spanning subgraphs of graphs with proper connection number 2. Theory Appl. Graphs 3(2), Art. 2 (2016)
Bondy, J.A., Murty, U.S.R.: Graph Theory. Graduate Texts in Mathematics, vol. 244. Springer, New York (2008)
Chang, H., Li, X., Magnant, C., Qin, Z.: The (k, ℓ)-proper index of graphs. arXiv:1606.03872v2
Chang, H., Li, X., Qin, Z.: Some upper bounds for the 3-proper index of graphs. Bull. Malays. Math. Sci. Soc. https://doi.org/10.1007/s40840-016-0404-5
Chartrand, G., Devereaux, S., Zhang, P.: Color-connection and information-transfer paths. Manuscript
Chen, L., Li, X., Liu, J.: The k-proper index of graphs. Appl. Math. Comput. 296, 57–63 (2017)
Coll, V., Hook, J., Magnant, C., McCready, K., Ryan, K.: Proper diameter of graphs. Discuss. Math. Graph Theory (to appear)
Devereaux, S., Johns, G., Zhang, P.: Color connection in graphs intermediate to proper and rainbow connection. Manuscript
Janson, S., Luczak, T., Ruciński, A.: Random Graphs. Wiley-Interscience Series in Discrete Mathematics and Optimization, xii+333 pp. Wiley, New York (2000)
Li, W., Li, X., Zhang, J.: The k-proper index of complete bipartite and complete multipartite graphs. Australas. J. Comb. 68(2), 304–316 (2017)
Li, X., Magnant, C., Wei, M., Zhu, X.: Distance proper connection of graphs. arXiv:1606.06547
Li, X., Magnant, C., Wei, M., Zhu, X.: Generalized rainbow connection of graphs and their complements. Discuss. Math. Graph Theory https://doi.org/10.7151/dmgt.2011
Melville R., Goddard, W.: Coloring graphs to produce properly colored walks. Graphs Comb. 33(5), 1271–1281 (2017)
Robbins, H.E.: A theorem on graphs, with an application to a problem of traffic control. Am. Math. Mon. 46, 281–283 (1939)
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Li, X., Magnant, C., Qin, Z. (2018). Other Generalizations. In: Properly Colored Connectivity of Graphs. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-89617-5_11
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DOI: https://doi.org/10.1007/978-3-319-89617-5_11
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