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Properly Colored Connectivity of Graphs pp 73–84Cite as

Proper k-Connection and Strong Proper Connection

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Abstract

Using a minimum degree assumption to provide density, the following was shown for pc 2(G). The proper 2-connection number pc 2(G) is the minimum number of colors needed to color the edges of G so that between every pair of vertices, there are at least two internally disjoint proper paths. First we present an easy lemma without proof.

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References

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Author information

Authors and Affiliations

  1. Center for Combinatorics, Nankai University, Tianjin, China

    Xueliang Li

  2. Department of Mathematics, Georgia Southern University, Statesboro, GA, USA

    Colton Magnant

  3. College of Science, Chang’an University, Xi’an, Shaanxi, China

    Zhongmei Qin

Authors
  1. Xueliang Li
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  2. Colton Magnant
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  3. Zhongmei Qin
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© 2018 The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature

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Li, X., Magnant, C., Qin, Z. (2018). Proper k-Connection and Strong Proper Connection. In: Properly Colored Connectivity of Graphs. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-89617-5_8

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