Abstract
Given a graph G, we study the problem of finding the minimum number of colors required for a proper edge coloring of G such that any pair of vertices at distance 2 have distinct sets consisting of colors of their incident edges. This minimum number is called the 2-distance vertex-distinguishing index, denoted by \(\chi '_{d2}(G)\). Using the breadth first search method, this paper provides a polynomial-time algorithm producing nearly-optimal solution in outerplanar graphs. More precisely, if G is an outerplanar graph with maximum degree \(\varDelta \), then the produced solution uses colors at most \(\varDelta +8\). Since \(\chi '_{d2}(G)\ge \varDelta \) for any graph G, our solution is within eight colors from optimal.
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Weifan Wang: Research supported by NSFC (No. 11371328).
Danjun Huang: Research supported by NSFC (Nos. 11301486, 11401535) and ZJNSFC (No. LQ13A010009).
Yiqiao Wang: Research supported by NSFC (No. 11301035).
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Wang, W., Huang, D., Wang, Y. et al. A polynomial-time nearly-optimal algorithm for an edge coloring problem in outerplanar graphs. J Glob Optim 65, 351–367 (2016). https://doi.org/10.1007/s10898-015-0360-x
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DOI: https://doi.org/10.1007/s10898-015-0360-x