Wyniki wyszukiwania

1

On the Schauder fixed point theorem

100%

Górniewicz L., Rozpłoch-Nowakowska D.

Banach Center Publications

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1996

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tom 35

|

nr 1

207-219

EN

The paper contains a survey of various results concerning the Schauder Fixed Point Theorem for metric spaces both in single-valued and multi-valued cases. A number of open problems is formulated.

2

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On the second largest eigenvalue of a mixed graph

100%

Zhou J., Fan Y.-Z., Wang Y.

Discussiones Mathematicae Graph Theory

|

2007

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tom 27

|

nr 2

373-384

EN

Let G be a mixed graph. We discuss the relation between the second largest eigenvalue λ₂(G) and the second largest degree d₂(G), and present a sufficient condition for λ₂(G) ≥ d₂(G).

3

Minimal vertex degree sum of a 3-path in plane maps

88%

Borodin O.

Discussiones Mathematicae Graph Theory

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1997

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tom 17

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nr 2

279-284

EN

Let wₖ be the minimum degree sum of a path on k vertices in a graph. We prove for normal plane maps that: (1) if w₂ = 6, then w₃ may be arbitrarily big, (2) if w₂ < 6, then either w₃ ≤ 18 or there is a ≤ 15-vertex adjacent to two 3-vertices, and (3) if w₂ < 7, then w₃ ≤ 17.

4

The Degree-Diameter Problem for Outerplanar Graphs

75%

Dankelmann P., Jonck E., Vetrík T.

Discussiones Mathematicae Graph Theory

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2017

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tom 37

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nr 3

823-834

EN

For positive integers Δ and D we define nΔ,D to be the largest number of vertices in an outerplanar graph of given maximum degree Δ and diameter D. We prove that [...] nΔ,D=ΔD2+O (ΔD2−1) $n_{\Delta ,D} = \Delta ^{{D \over 2}} + O\left( {\Delta ^{{D \over 2} - 1} } \right)$ is even, and [...] nΔ,D=3ΔD−12+O (ΔD−12−1) $n_{\Delta ,D} = 3\Delta ^{{{D - 1} \over 2}} + O\left( {\Delta ^{{{D - 1} \over 2} - 1} } \right)$ if D is odd. We then extend our result to maximal outerplanar graphs by showing that the maximum number of vertices in a maximal outerplanar graph of maximum degree Δ and diameter D asymptotically equals nΔ,D.

5

Equivariant Nielsen theory

75%

Wong P.

Banach Center Publications

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1999

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tom 49

|

nr 1

253-258

6

Some applications of pq-groups in graph theory

75%

Exoo G.

Discussiones Mathematicae Graph Theory

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2004

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tom 24

|

nr 1

109-114

EN

We describe some new applications of nonabelian pq-groups to construction problems in Graph Theory. The constructions include the smallest known trivalent graph of girth 17, the smallest known regular graphs of girth five for several degrees, along with four edge colorings of complete graphs that improve lower bounds on classical Ramsey numbers.

7

Open maps between Knaster continua

75%

Eberhart C., Fugate J. B., Schumann S.

Fundamenta Mathematicae

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1999

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tom 162

|

nr 2

119-148

EN

We investigate the set of open maps from one Knaster continuum to another. A structure theorem for the semigroup of open induced maps on a Knaster continuum is obtained. Homeomorphisms which are not induced are constructed, and it is shown that the induced open maps are dense in the space of open maps between two Knaster continua. Results about the structure of the semigroup of open maps on a Knaster continuum are obtained and two questions about the structure are posed.

Ograniczanie wyników

4 Discussiones Mathematicae Graph Theory

2 Banach Center Publications

1 Fundamenta Mathematicae

1 Borodin O.

1 Dankelmann P.

1 Eberhart C.

1 Exoo G.

1 Fan Y.-Z.

1 Fugate J. B.

1 Górniewicz L.

1 Jonck E.

1 Rozpłoch-Nowakowska D.

1 Schumann S.

1 Vetrík T.

1 Wang Y.

1 Wong P.

1 Zhou J.

1 2017

1 2007

1 2004

2 1999

1 1997

1 1996

On the Schauder fixed point theorem

On the second largest eigenvalue of a mixed graph

Minimal vertex degree sum of a 3-path in plane maps

The Degree-Diameter Problem for Outerplanar Graphs

Equivariant Nielsen theory

Some applications of pq-groups in graph theory

Open maps between Knaster continua