Journal Article10.1007/BF02024498
On maximal paths and circuits of graphs
907
About: This article is published in Acta Mathematica Hungarica. The article was published on 01 Sep 1959.
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Citations
Monochromatic Hamiltonian t-tight Berge-cycles in hypergraphs
TL;DR: In this paper, the authors formulate the following conjecture: for any fixed 2 ≤ c, t ≤ r satisfying c + t ≤ c ≤ r and sufficiently large n, if we color the edges of Kn(r), the complete r-uniform hypergraph on n vertices, with c colors, then there is a monochromatic Hamiltonian t-tight Berge-cycle.
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Eigenvalues and forbidden subgraphs I
TL;DR: In this article, the number of vertices, edges, and triangles of a graph is related to the smallest eigenvalue of its adjacency matrix and the largest eigen value of its Laplacian.
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The Ramsey numbers of wheels versus odd cycles
TL;DR: It is shown that R(W"n,C"m)=2n+1 for m odd, n>=3(m-1)/2 and (m,n) (3,3),(3,4), and R(w, n, C"m) =3m-2 for m,n odd and m.
12
Ramsey numbers for brooms
Péter L. Erdős,Ralph J. Faudree +1 more
- 01 Jan 1982
TL;DR: A broom Bk,k is a tree obtained by identifying an end- vertex o£ a path on k vertices with the central vertex of star on k edges.
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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.