Geodesic
Star Coloring Outerplanar Bipartite Graphs
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 4, pp. 899-908

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A proper coloring of the vertices of a graph is called a star coloring if at least three colors are used on every 4-vertex path. We show that all outerplanar bipartite graphs can be star colored using only five colors and construct the smallest known example that requires five colors.
Keywords: chromatic number, star coloring, outerplanar bipartite graph 
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     author = {Ramamurthi, Radhika and Sanders, Gina},
     title = {Star {Coloring} {Outerplanar} {Bipartite} {Graphs}},
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Ramamurthi, Radhika; Sanders, Gina. Star Coloring Outerplanar Bipartite Graphs. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 4, pp. 899-908. http://geodesic.mathdoc.fr/item/DMGT_2019_39_4_a10/