Journal Article10.1007/BF02024498
On maximal paths and circuits of graphs
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About: This article is published in Acta Mathematica Hungarica. The article was published on 01 Sep 1959.
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Citations
•Posted Content
Tight paths in convex geometric hypergraphs
TL;DR: In this paper, a theorem on tight paths in convex geometric hypergraphs, which is asymptotically sharp in infinitely many cases, was proved and shown to be a generalization of Hopf and Pannwitz, Sutherland, Kupitz and Perles.
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Hypergraphs not containing a tight tree with a bounded trunk II: 3-trees with a trunk of size 2
TL;DR: Furedi et al. as mentioned in this paper proved the exact form of Kalai's Conjecture for all tight 3-trees of at least 8 edges that have a trunk of size two.
Large Circuits in Binary Matroids of Large Cogirth, I
TL;DR: It is shown that ifMdoes not have anF7-minor,M?F*7, andd?(r(M)+1)/2 thenMhas a circuit of sizer(M)-1, and ifMis connected,e?E(M),M does not have both anF8- Minor and anF*8-Minor, thenM has a circuit that containse and has size at leastd+1.
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•Posted Content
Turán's Problem for Trees
Zhi-Wei Sun,Lin-Lin Wang +1 more
TL;DR: In this article, the maximal number of edges in a simple graph of order not containing a forbidden graph was defined as a tree with maximal degree n-2, and exact values of $ex(p;T_n)$ and $ex (p; T_n^*) were given.
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Large matchings in uniform hypergraphs and the conjectures of Erdos and Samuels
TL;DR: This paper asymptotically determine the minimum vertex degree which guarantees a perfect matching in 4- uniform and 5-uniform hypergraphs and obtains some general theorems on the minimum d-degree ensuring the existence of perfect (fractional) matchings.
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References
On the structure of linear graphs
Paul Erdös,A. H. Stone +1 more
TL;DR: The first result in this direction was due to Turân as discussed by the authors, who proved that a graph with kn vertices and Ck, 2n+1 edges always contains a complete graph of order k + 1.