منابع مشابه
Removable Circuits in Multigraphs
We prove the following conjecture of Bill Jackson ( J. London Math. Soc. (2) 21 (1980) p. 391). If G is a 2-connected multigraph with minimum degree at least 4 and containing no Petersen minor, then G contains a circuit C such that G E(C) is 2-connected. In fact, G has at least two edge-disjoint circuits which can serve as C. Until now, the conjecture had been veri ed only for planar graphs and...
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We show that if M is a connected binary matroid of cogirth at least ve which does not have both an F 7-minor and an F 7-minor, then M has a circuit C such that M ? C is connected and r(M ? C) = r(M).
متن کاملOn fans in multigraphs
We introduce a unifying framework for studying edge-colouring problems on multigraphs. This is defined in terms of a rooted directed multigraph F which is naturally associated to the set of fans based at a given vertex u in a multigraph G. We call F the “Fan Digraph”. We show that fans in G based at u are in one-to-one correspondence with directed trails in F starting at the root of F . We stat...
متن کاملRainbow matchings in bipartite multigraphs
Suppose that k is a non-negative integer and a bipartite multigraph G is the union of N = ⌊ k + 2 k + 1 n ⌋ − (k + 1) matchings M1, . . . ,MN , each of size n. We show that G has a rainbow matching of size n− k, i.e. a matching of size n− k with all edges coming from different Mi’s. Several choices of parameters relate to known results and conjectures. Suppose that a multigraph G is given with ...
متن کاملCycles and paths in multigraphs
We consider cycles and paths in multigraphic realizations of a degree sequence Q. in particular we show that there exists a realization of d in which no cycle has order greater than three and no path has length greater than four. In addition we show which orders of cycles and which lengths of paths exist in some realization of d.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1997
ISSN: 0095-8956
DOI: 10.1006/jctb.1997.1775