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
On three-color Ramsey numbers R(C4,K1,m,Pn)
TL;DR: By discussing the local structure of the polarity graph whose vertices are points in the projective plane over Galois fields, it is shown that the two upper bounds can be attained for some special m and n.
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The (p,q)-extremal problem and the fractional chromatic number of Kneser hypergraphs
TL;DR: The ( p, q ) -extremal problem for graphs is solved and with the aid of this result the fractional chromatic number of Kneser hypergraphs when they are composed with sets of cardinality 2 is calculated.
Long paths and cycles passing through specified vertices under the average degree condition
TL;DR: In this article, it was shown that for two distinct vertices (x and z) in a graph G, there exists a cycle of length at least 2m/(n-1) passing through any vertex other than x and z. This result generalizes a theorem of Fan on the existence of long cycles under the average degree condition.
On the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mi>A</mml:mi><mml:mi>α</mml:mi></mml:msub></mml:math>-spectral radius of graphs without linear forests
TL;DR: In this article , the maximum signless Laplacian spectral radius of graphs on n vertices without a subgraph isomorphic to a linear forest for a real number α ∈ [0, 1] is derived.
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.