Wszystkie pola: Ramsey numbers - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Planar Ramsey numbers
Autorzy:: Gorgol, Izolda
Powiązania:: https://bibliotekanauki.pl/articles/744298.pdf
Data publikacji:: 2005
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: Ramsey number
planar graph
induced subgraph
Opis:: The planar Ramsey number PR(G,H) is defined as the smallest integer n for which any 2-colouring of edges of Kₙ with red and blue, where red edges induce a planar graph, leads to either a red copy of G, or a blue H. In this note we study the weak induced version of the planar Ramsey number in the case when the second graph is complete.
Źródło:: Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 45-50
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: A Note on Lower Bounds for Induced Ramsey Numbers
Autorzy:: Gorgol, Izolda
Powiązania:: https://bibliotekanauki.pl/articles/31343354.pdf
Data publikacji:: 2019-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: induced Ramsey number
Opis:: We say that a graph $F$ strongly arrows a pair of graphs $(G,H)$ and write $ F \xrightarrow{ind} (G,H) $ if any 2-coloring of its edges with red and blue leads to either a red $G$ or a blue $H$ appearing as induced subgraphs of $F$. The induced Ramsey number, $ IR(G,H) $ is defined as $ \min \{ |V (F)| : F \xrightarrow{ind} $ $ (G,H) \} $. We will consider two aspects of induced Ramsey numbers. Firstly we will show that the lower bound of the induced Ramsey number for a connected graph $G$ with independence number $ \alpha $ and a graph $H$ with clique number $ \omega $ is roughly $ \tfrac{ \omega^2 \alpha } { 2 } $. This bound is sharp. Moreover we will also consider the case when $G$ is not connected providing also a sharp lower bound which is linear in both parameters.
Źródło:: Discussiones Mathematicae Graph Theory; 2019, 39, 3; 647-654
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Rainbow numbers for small stars with one edge added
Autorzy:: Gorgol, Izolda
Łazuka, Ewa
Powiązania:: https://bibliotekanauki.pl/articles/744067.pdf
Data publikacji:: 2010
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: rainbow number
anti-Ramsey number
Opis:: A subgraph of an edge-colored graph is rainbow if all of its edges have different colors. For a graph H and a positive integer n, the anti-Ramsey number f(n,H) is the maximum number of colors in an edge-coloring of Kₙ with no rainbow copy of H. The rainbow number rb(n,H) is the minimum number of colors such that any edge-coloring of Kₙ with rb(n,H) number of colors contains a rainbow copy of H. Certainly rb(n,H) = f(n,H) + 1. Anti-Ramsey numbers were introduced by Erdös et al. [5] and studied in numerous papers.
We show that $rb(n,K_{1,4} + e) = n + 2$ in all nontrivial cases.
Źródło:: Discussiones Mathematicae Graph Theory; 2010, 30, 4; 555-562
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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