منابع مشابه
Solis Graphs and Uniquely Metric Basis Graphs
A set $Wsubset V (G)$ is called a resolving set, if for every two distinct vertices $u, v in V (G)$ there exists $win W$ such that $d(u,w) not = d(v,w)$, where $d(x, y)$ is the distance between the vertices $x$ and $y$. A resolving set for $G$ with minimum cardinality is called a metric basis. A graph with a unique metric basis is called a uniquely dimensional graph. In this paper, we establish...
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The key to Seymour’s Regular Matroid Decomposition Theorem is his result that each 3-connected regular matroid with no R10or R12-minor is graphic or cographic. We present a proof of this in terms of signed graphs. 2004 Wiley Periodicals, Inc. J Graph Theory 48: 74–84, 2005
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We relate matroid connectivity to Tutte-connectivity in an infinite graph. Moreover, we show that the two cycle matroids, the finite-cycle matroid and the cycle matroid, in which also infinite cycles are taken into account, have the same connectivity function. As an application we re-prove that, also for infinite graphs, Tutte-connectivity is invariant under taking dual graphs.
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The independent assignment problem (or the weighted matroid intersection problem) is extended using Dress-Wenzel’s matroid valuations, which are attached to the vertex set of the underlying bipartite graph as an additional weighting. Specifically, the problem considered is: Given a bipartite graph G = (V , V −;A) with arc weight w : A → R and matroid valuations ω and ω− on V + and V − respectiv...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1973
ISSN: 0095-8956
DOI: 10.1016/0095-8956(73)90005-1