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Infinitely Many Trees with Maximum Number of Holes Zero, One, and Two
(Hindawi Limited, 2018) Kola, S.R.; Gudla, B.; Niranjan, P.K.
An L(2,1)-coloring of a simple connected graph G is an assignment f of nonnegative integers to the vertices of G such that fu-fv2 if d(u,v)=1 and fu-fv1 if d(u,v)=2 for all u,v∈V(G), where d(u,v) denotes the distance between u and v in G. The span of f is the maximum color assigned by f. The span of a graph G, denoted by (G), is the minimum of span over all L(2,1)-colorings on G. An L(2,1)-coloring of G with span (G) is called a span coloring of G. An L(2,1)-coloring f is said to be irreducible if there exists no L(2,1)-coloring g such that g(u)f(u) for all u∈V(G) and g(v)