The hamiltonicity and path -coloring of Sierpiński-like graphs
摘要：
A mapping from V(G) to {1,2,…,t} is called a patht-coloring of a graph G if each G[1(i)], for 1≤i≤t, is a linear forest. The vertex linear arboricity of a graph G, denoted by vla(G), is the minimum t for which G has a path t-coloring. Graphs S[n,k] are obtained from the Sierpiński graphs S(n,k) by contracting all edges that lie in no induced Kk. In this paper, the hamiltonicity and path t-coloring of Sierpiński-like graphs S(n,k), S+(n,k), S++(n,k) and graphs S[n,k] are studied. In particular, it is obtained that vla(S(n,k))=vla(S[n,k])=k/2 for k≥2. Moreover, the numbers of edge disjoint Hamiltonian paths and Hamiltonian cycles in S(n,k), S+(n,k) and S++(n,k) are completely determined, respectively.
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DOI：
10.1016/j.dam.2012.03.022
被引量：
年份：
2012
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