منابع مشابه
Cycle spectra of Hamiltonian graphs
We prove that every Hamiltonian graph with n vertices and m edges has cycles of at least √ 4 7(m − n) different lengths. The coefficient 4/7 cannot be increased above 1, since when m = n2/4 there are √ m − n + 1 cycle lengths in Kn/2,n/2. For general m and n there are examples having at most 2 ⌈
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For any h in N , a graph G = (V, E) is said to be h-magic if there exists a labeling l: E(G) to Z_{h}-{0} such that the induced vertex set labeling l^{+: V(G) to Z_{h}} defined by l^{+}(v)= Summation of l(uv)such that e=uvin in E(G) is a constant map. For a given graph G, the set of all for which G is h-magic is called the integer-magic spectrum of G and is denoted by IM(G). In this paper, the ...
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This thesis contains several new results about cycle spectra of graphs. The cycle spectrum of a graph G is the set of lengths of cycles in G. We focus on conditions which imply a rich cycle spectrum. We show a lower bound for the size of the cycle spectrum of cubic Hamiltonian graphs that do not contain a fixed subdivision of a claw as an induced subgraph. Furthermore, we consider cycle spectra...
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If π is a cyclic order of the vertices of a graph G, the number h(π) is defined to be the sum of the distances between consecutive vertices of G in π. For a graph G, the hamiltonian spectrum H(G) is the set of all numbers h(π). The hamiltonian number h(G) of G is the minimum number contained in H(G) and the upper hamiltonian number h+(G) is the maximum number contained in H(G). We determine ham...
متن کاملHamiltonian Cycle Problem for Triangle Graphs
We show that the Hamiltonian cycle problem is NP-complete for a class of planar graphs named triangle graphs that are closely related to inner-triangulated graphs. We present a linear-time heuristic algorithm that nds a solution at most one-third longer than the optimum solution and use it to obtain a fast rendering algorithm on triangular meshes in computer graphics.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2012
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2012.04.002