Powers of cycles, powers of paths, and distance graphs
نویسندگان
چکیده
منابع مشابه
Powers of cycles, powers of paths, and distance graphs
In 1988, Golumbic and Hammer characterized powers of cycles, relating them to circular-arc graphs. We extend their results and propose several further structural characterizations for both powers of cycles and powers of paths. The characterizations lead to linear-time recognition algorithms of these classes of graphs. Furthermore, as a generalization of powers of cycles, powers of paths, and ev...
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The Kronecker product of two connected graphs G1,G2, denoted by G1 × G2, is the graph with vertex set V (G1 ×G2) = V (G1)×V (G2) and edge set E(G1 ×G2) = {(u1, v1)(u2, v2) : u1u2 ∈ E(G1), v1v2 ∈ E(G2)}. The kth power Gk of G is the graph with vertex set V (G) such that two distinct vertices are adjacent in Gk if and only if their distance apart in G is at most k. A connected graph G is called s...
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متن کاملPowers of Hamilton Cycles in Pseudorandom Graphs
We study the appearance of powers of Hamilton cycles in pseudorandom graphs, using the following comparatively weak pseudorandomness notion. A graph G is (ε, p, k, l)-pseudorandom if for all disjoint X and Y ⊆ V (G) with |X| ≥ εpkn and |Y | ≥ εpln we have e(X,Y ) = (1± ε)p|X||Y |. We prove that for all β > 0 there is an ε > 0 such that an (ε, p, 1, 2)-pseudorandom graph on n vertices with minim...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2011
ISSN: 0166-218X
DOI: 10.1016/j.dam.2010.03.012