Results 231 to 240 of about 17,750 (263)
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Canadian Journal of Mathematics, 1964
It is well known that for finite connected graphs the following are equivalent:(i)X is Euler (i.e., every vertex of X has positive even degree);(ii)X is traceable (i.e., the edges of X can be arranged in a sequence e1, . . . ,en such that ei ≠ ej if i ≠ j, and ei, ei+1 are adjacent, i = 1, . . .
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It is well known that for finite connected graphs the following are equivalent:(i)X is Euler (i.e., every vertex of X has positive even degree);(ii)X is traceable (i.e., the edges of X can be arranged in a sequence e1, . . . ,en such that ei ≠ ej if i ≠ j, and ei, ei+1 are adjacent, i = 1, . . .
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The Spectrum of an Infinite Graph
Canadian Journal of Mathematics, 2000AbstractIn this paper, we consider the (essential) spectrum of the discrete Laplacian of an infinite graph. We introduce a new quantity for an infinite graph, in terms of which we give new lower bound estimates of the (essential) spectrum and give also upper bound estimates when the infinite graph is bipartite. We give sharp estimates of the (essential)
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On self‐immersions of infinite graphs
Journal of Graph Theory, 2008AbstractThe existence of an infinite graph which is not isomorphic to a proper minor of itself was proved by Oporowski. In the present note, it is shown that an analogous result holds when immersions are considered instead of minors. The question whether or not the same is true for weak immersions remains open. © 2008 Wiley Periodicals, Inc.
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Infinite Sets and Infinite Graphs
1985E.C. MILNER: Let me begin with a problem due to Prikry and myself. First I’ll state a theorem concerning the depth of an ordered set. The depth of a partial order is the least ordinal γ such that does not embed γ*, the reverse of γ. For example vK has depth v+, if v ⪰ ω, κ ⪰ 2.
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The Cycle Space of an Infinite Graph
Combinatorics, Probability and Computing, 2005Finite graph homology may seem trivial, but for infinite graphs things become interesting. We present a new ‘singular’ approach that builds the cycle space of a graph not on its finite cycles but on its topological circles, the homeomorphic images of $S^1$ in the space formed by the graph together with its ends. Our approach permits the extension to
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On highly ramsey infinite graphs
Journal of Graph Theory, 2008AbstractWe show that, for r ≥ 2 and k ≥ 3, there exists a positive constant c such that for large enough n there are 2 non‐isomorphic graphs on at most n vertices that are r‐ramsey‐minimal for the odd cycle C2k+1. © 2008 Wiley Periodicals, Inc.
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1990
Given a graph \(G\), a covering of \(G\) is a set of subgraphs \(\{G_ 1,G_ 2,\dots,G_ k\}\) such that every edge of \(G\) is in some \(G_ i\). A set of edges \(\{e_ 1,e_ 2,\dots,e_ k\}\) with \(e_ i\in E(G_ i)\) is called a set of distinct representing edges. \textit{L.
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Given a graph \(G\), a covering of \(G\) is a set of subgraphs \(\{G_ 1,G_ 2,\dots,G_ k\}\) such that every edge of \(G\) is in some \(G_ i\). A set of edges \(\{e_ 1,e_ 2,\dots,e_ k\}\) with \(e_ i\in E(G_ i)\) is called a set of distinct representing edges. \textit{L.
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A greedy algorithm for finding maximum spanning trees in infinite graphs
Operations Research Letters, 2022Christopher Thomas Ryan, Robert L Smith
exaly