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Displaying similar documents to “Equilateral triangles in finite metric spaces.”

Cycles through specified vertices in triangle-free graphs

Daniel Paulusma, Kiyoshi Yoshimoto (2007)

Discussiones Mathematicae Graph Theory

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Let G be a triangle-free graph with δ(G) ≥ 2 and σ₄(G) ≥ |V(G)| + 2. Let S ⊂ V(G) consist of less than σ₄/4+ 1 vertices. We prove the following. If all vertices of S have degree at least three, then there exists a cycle C containing S. Both the upper bound on |S| and the lower bound on σ₄ are best possible.

Fixed-point free maps of Euclidean spaces

R. Z. Buzyakova, A. Chigogidze (2011)

Fundamenta Mathematicae

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Our main result states that every fixed-point free continuous self-map of ℝⁿ is colorable. This result can be reformulated as follows: A continuous map f: ℝⁿ → ℝⁿ is fixed-point free iff f̃: βℝⁿ → βℝⁿ is fixed-point free. We also obtain a generalization of this fact and present some examples

On the Erdős-Gyárfás Conjecture in Claw-Free Graphs

Pouria Salehi Nowbandegani, Hossein Esfandiari, Mohammad Hassan Shirdareh Haghighi, Khodakhast Bibak (2014)

Discussiones Mathematicae Graph Theory

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The Erdős-Gyárfás conjecture states that every graph with minimum degree at least three has a cycle whose length is a power of 2. Since this conjecture has proven to be far from reach, Hobbs asked if the Erdős-Gyárfás conjecture holds in claw-free graphs. In this paper, we obtain some results on this question, in particular for cubic claw-free graphs