A graph-theoretic proof of Sharkovsky’s theorem on the periodic points of continuous functions

It is known that two commuting continuous functions on an interval need not have a common fixed point. It is not known if such two functions have a common periodic point. In this paper we first give some results in this direction. We then define a new contractive condition, under which two continuous functions must have a unique common fixed point.

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Tree enterprises and bankruptcy ventures A game theoretic similarity due to a graph theoretic proof

Discrete Applied Mathematics ◽

10.1016/s0166-218x(97)00036-x ◽

1997 ◽

Vol 79 (1-3) ◽

pp. 105-117

Author(s):

Theo S.H. Driessen

Keyword(s):

Graph Theoretic ◽

Theoretic Proof ◽

Game Theoretic

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Counting degree sequences of spanning trees in bipartite graphs: A graph‐theoretic proof

Journal of Graph Theory ◽

10.1002/jgt.22449 ◽

2019 ◽

Vol 92 (3) ◽

pp. 230-236

Author(s):

Anja Fischer ◽

Frank Fischer

Keyword(s):

Spanning Trees ◽

Bipartite Graphs ◽

Degree Sequences ◽

Graph Theoretic ◽

Theoretic Proof

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Periodic Points of Continuous Functions

Mathematics Magazine ◽

10.1080/0025570x.1978.11976687 ◽

1978 ◽

Vol 51 (2) ◽

pp. 99-105 ◽

Cited By ~ 18

Author(s):

Philip D. Straffin

Keyword(s):

Periodic Points ◽

Continuous Functions

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On the Number of Orthogonal Systems in Vector Spaces over Finite Fields

The Electronic Journal of Combinatorics ◽

10.37236/907 ◽

2008 ◽

Vol 15 (1) ◽

Cited By ~ 6

Author(s):

Le Anh Vinh

Keyword(s):

Finite Field ◽

Vector Space ◽

Finite Fields ◽

Vector Spaces ◽

Dimensional Vector ◽

Dimensional Vector Space ◽

Graph Theoretic ◽

Theoretic Proof ◽

Orthogonal Systems

Iosevich and Senger (2008) showed that if a subset of the $d$-dimensional vector space over a finite field is large enough, then it contains many $k$-tuples of mutually orthogonal vectors. In this note, we provide a graph theoretic proof of this result.

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