On path connected graphs
نویسندگان
چکیده
منابع مشابه
Connected but not path-connected subspaces of infinite graphs
Solving a problem of Diestel [8] we show that the Freudenthal compactification of a locally finite graph can have connected subsets that are not path-connected. However we prove that connectedness and pathconnectedness do coincide for all but a few sets, which have a complicated structure.
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It is known that the list of excluded minors for the minor-closed class of graphs of path-width 6 3 numbers in the millions. However, if we restrict the class to 3-connected graphs of path-width 6 3, then we can characterize it by five excluded minors.
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Menger's Theorem states that in a 3-connected graph, any two vertices are joined by three openly disjoint paths. Here we consider 3-connected cubic graphs where two vertices exist so that the three disjoint paths between them contain all of the vertices of the graph (we call these graphs 3*connected); and also where the latter is true for ALL pairs of vertices (globally 3*-connected). A necessa...
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متن کاملMinors of two-connected graphs of large path-width
Let P be a graph with a vertex v such that P\v is a forest, and let Q be an outerplanar graph. We prove that there exists a number p = p(P,Q) such that every 2-connected graph of path-width at least p has a minor isomorphic to P or Q. This result answers a question of Seymour and implies a conjecture of Marshall and Wood.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1978
ISSN: 0095-8956
DOI: 10.1016/0095-8956(78)90001-1