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(2007)
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A.N.M. Salman, H.J. Broersma, J. Fujisawa, L. Marchal, D. Paulusma, K. Yoshimoto (2009)
λ-Backbone coloring along pairwise disjoint stars and matchingsDiscrete Math., 309
J.A. Bondy, U.S.R. Murty (2008)
Graph Theory
Weifan Wang, Y. Bu, M. Montassier, A. Raspaud (2012)
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H. Broersma, J. Fujisawa, Kiyoshi Yoshimoto (2003)
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B. Hajo, V. F. Fador, A. G. Petr, J. Wo.eginger Gerhard (2003)
Backbone Coloring for Networks
Let G be a graph and H a subgraph of G. A backbone-k-coloring of (G, H) is a mapping f: V(G) → {1, 2, ···, k} such that |f(u) − f(v)| ≥ 2 if uv ∈ E(H) and |f(u) − f(v)| ≥ 1 if uv ∈ E(G)E(H). The backbone chromatic number of (G, H) denoted by χ b (G, H) is the smallest integer k such that (G, H) has a backbone-k-coloring. In this paper, we prove that if G is either a connected triangle-free planar graph or a connected graph with mad(G) < 3, then there exists a spanning tree T of G such that χ b (G, T) ≤ 4.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Aug 7, 2017
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