Displaying similar documents to “Voltage graphs, group presentations and cages.”

Dynamic cage survey.

Exoo, Geoffrey, Jajcay, Robert (2008)

The Electronic Journal of Combinatorics [electronic only]

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A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs

Wojciech Wide (2017)

Discussiones Mathematicae Graph Theory

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A graph G on n vertices is said to be pancyclic if it contains cycles of all lengths k for k ∈ {3, . . . , n}. A vertex v ∈ V (G) is called super-heavy if the number of its neighbours in G is at least (n+1)/2. For a given graph H we say that G is H-f1-heavy if for every induced subgraph K of G isomorphic to H and every two vertices u, v ∈ V (K), dK(u, v) = 2 implies that at least one of them is super-heavy. For a family of graphs H we say that G is H-f1-heavy, if G is H-f1-heavy for...

The cycle-complete graph Ramsey number r(C₅,K₇)

Ingo Schiermeyer (2005)

Discussiones Mathematicae Graph Theory

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The cycle-complete graph Ramsey number r(Cₘ,Kₙ) is the smallest integer N such that every graph G of order N contains a cycle Cₘ on m vertices or has independence number α(G) ≥ n. It has been conjectured by Erdős, Faudree, Rousseau and Schelp that r(Cₘ,Kₙ) = (m-1)(n-1)+1 for all m ≥ n ≥ 3 (except r(C₃,K₃) = 6). This conjecture holds for 3 ≤ n ≤ 6. In this paper we will present a proof for r(C₅,K₇) = 25.