Search CORE

1,720,957 research outputs found

The $m$ -bipartite Ramsey number $BR_m(H_1,H_2)$

Author: Rowshan Yaser
Publication venue
Publication date: 01/01/2024
Field of study

In a

(G^1,G^2)

coloring of a graph

G

, every edge of

G

is in

G^1

G^2

. For two bipartite graphs

H_1

and

H_2

, the bipartite Ramsey number

BR(H_1, H_2)

is the least integer

b\geq 1

, such that for every

(G^1, G^2)

coloring of the complete bipartite graph

K_{b,b}

, results in either

H_1\subseteq G^1

H_2\subseteq G^2

. As another view, for bipartite graphs

H_1

and

H_2

and a positive integer

m

, the

m

-bipartite Ramsey number

BR_m(H_1, H_2)

H_1

and

H_2

is the least integer

n

(n\geq m)

such that every subgraph

G

K_{m,n}

results in

H_1\subseteq G

H_2\subseteq \overline{G}

. The size of

m

-bipartite Ramsey number

BR_m(K_{2,2}, K_{2,2})

, the size of

m

-bipartite Ramsey number

BR_m(K_{2,2}, K_{3,3})

and the size of

m

-bipartite Ramsey number

BR_m(K_{3,3}, K_{3,3})

have been computed in several articles up to now. In this paper we determine the exact value of

BR_m(K_{2,2}, K_{4,4})

for each

m\geq 2

Biblioteka Nauki - repozytorium artykuÅÃ³w

Vertex Partitions and Maximum \G-free Subgraphs

Author: Rowshan Yaser
Publication venue
Publication date: 03/09/2023
Field of study

We define a

(V_1, V_2, \ldots, V_k)

-partition for a given graph

H

and graphical properties

P_1, P_2, \ldots, P_k

as a partition where each

V_i

induces a subgraph of

H

with property

P_i

. Matamala (2007) extended this result by showing that for any graph

H

with

\Delta(H)=p+q

, there exists a

(V_1, V_2)

-partition of

V(H)

where

H[V_1]

is a maximum order

(p-1)

-degenerate induced subgraph and

H[V_2]

(q-1)

-degenerate. Additionally, Catlin and Lai proved that if

\Delta(H)\geq 5

H

has a

(V_1, V_2)

-partition such that

H[V_1]

is a maximum order acyclic induced subgraph,

\omega(H[V_2])\leq \Delta(H)-2

, and

\Delta(H[V_2])\leq \Delta(H)-2

. Rowshan and Taherkhani demonstrated that given a graph

G

with a minimum degree

\delta(G)

and for

k=\lceil \frac{\Delta(H)}{\delta(G)}\rceil

, there exists a

(V_1, V_2, \ldots, V_k)

-partition of the vertex set of

H

, such that each

H[V_i]

G

-free, meaning it does not contain a subgraph isomorphic to

G

, and

H[V_1]

is a maximum order

G

-free induced subgraph. In our paper, we present a novel result for a connected graph

H

with

\Delta(H)\geq 5

and without

K_{\Delta(H)+1}\setminus e

as a subgraph. We establish that when

p_1\geq p_2\geq\cdots\geq p_{k-1}\geq 2

p_k\geq 4

\sum_{i=1}^k p_i=\Delta(H)-1+k

, and

\mathcal{G}_i

represents a family of graphs with a minimum degree at least

p_i-1

for each

i\in [k-1]

, a

(V_1, V_2, \ldots, V_k)

-partition of

V(H)

exists. This partition guarantees that

H[V_1]

is a maximum order

\mathcal{G}_1

-free induced subgraph,

H[V_i]

\mathcal{G}_i

-free for each

2\leq i\leq k-1

\Delta(H[V_k])\leq p_k

, and either

H[V_k]

K_{p_k}

-free or its

p_k

-cliques are disjoint

arXiv.org e-Print Archive

The $m$ -bipartite Ramsey number $BR_m(K_{2,2},K_{5,5})$

Author: Rowshan Yaser
Publication venue
Publication date: 02/08/2023
Field of study

The bipartite Ramsey number

BR(H_1,H_2,\ldots,H_k)

, is the smallest positive integer

b

, such that each

k

-decomposition of

E(K_{b,b})

contains

H_i

in the

i

-th class for some

i, 1\leq i\leq k

. As another view of bipartite Ramsey numbers, for given two bipartite graphs

H_1

and

H_2

and a positive integer

m

, the

m

-bipartite Ramsey number

BR_m(H_1, H_2)

, is defined as the least integer

n

, such that any subgraph of

K_{m,n}

say

H

, results in

H_1\subseteq H

H_2\subseteq \overline{H}

. The size of

BR_m(K_{2,2}, K_{3,3})

BR_m(K_{2,2}, K_{4,4})

for each

m

, and the size of

BR_m(K_{3,3}, K_{3,3})

for some

m

, have been determined in several papers up to now. Also, it is shown that

BR(K_{2,2}, K_{5,5})=17

. In this article, we compute the size of

BR_m(K_{2,2}, K_{5,5})

for some

m\geq 2

arXiv.org e-Print Archive

Borodin-Kostochka conjecture and Partitioning a graph into classes with no clique of specified size

Author: Rowshan Yaser
Publication venue
Publication date: 15/11/2023
Field of study

For a given graph

H

and the graphical properties

P_1, P_2,\ldots,P_k

, a graph

H

is said to be

(V_1, V_2,\ldots,V_k)

-partitionable if there exists a partition of

V(H)

into

k

-sets

V_1, V_2\ldots,V_k

, such that for each

i\in[k]

, the subgraph induced by

V_i

has the property

P_i

. In

1979

, Bollob\'{a}s and Manvel showed that for a graph

H

with maximum degree

\Delta(H)\geq 3

and clique number

\omega(H)\leq \Delta(H)

, if

\Delta(H)= p+q

, then there exists a

(V_1,V_2)

-partition of

V(H)

, such that

\Delta(H[V_1])\leq p

\Delta(H[V_2])\leq q

H[V_1]

(p-1)

-degenerate, and

H[V_2]

(q-1)

-degenerate. Assume that

p_1\geq p_2\geq\cdots\geq p_k\geq 2

are

k

positive integers and

\sum_{i=1}^k p_i=\Delta(H)-1+k

. Assume that for each

i\in[k]

the properties

P_i

means that

\omega(H[V_i])\leq p_i-1

. Is

H

(V_1,\ldots,V_k)

-partitionable graph? In 1977, Borodin and Kostochka conjectured that any graph

H

with maximum degree

\Delta(H)\geq 9

and without

K_{\Delta(H)}

as a subgraph, has chromatic number at most

\Delta(H)-1

. Reed proved that the conjecture holds whenever

\Delta(G) \geq 10^{14}

. When

p_1=2

and

\Delta(H)\geq 9

, the above question is the Borodin and Kostochka conjecture. Therefore, when all

p_i

s are equal to

2

and

\Delta(H)\leq 8

, the answer to the above question is negative. Let

H

is a graph with maximum degree

\Delta

, and clique number

\omega(H)

, where

\omega(H)\leq \Delta-1

. In this article, we intend to study this question when

k\geq 2

and

\Delta\geq 13

. In particular as an analogue of the Borodin-Kostochka conjecture, for the case that

\Delta\geq 13

and

p_i\geq 2

we prove that the above question is true

arXiv.org e-Print Archive

Author Instructions

Author: Instructions Author
Publication venue
Publication date: 04/11/2013
Field of study

Crossref

Cartographic Perspectives (E-Journal - North American Cartographic Information Society, NACIS)

Going Beyond Counting First Authors in Author Co-citation Analysis

Author: Zhao Dangzhi
Publication venue
Publication date: 01/01/2005
Field of study

The present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed

E-LIS

Variations on the Author

Author: Sayad Cecilia
Publication venue
Publication date: 01/01/2016
Field of study

“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship

Crossref

Kent Academic Repository

Appropriate Similarity Measures for Author Cocitation Analysis

Author: Waltman L.R.
Eck N.J.P. van
Publication venue
Publication date
Field of study

We provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authorsâ€™ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis

Research Papers in Economics

Dispelling the Myths Behind First-author Citation Counts

Author: Zhao Dangzhi
Publication venue
Publication date: 01/01/2006
Field of study

We conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more sophisticated methods

E-LIS

Author Index

Author: Author Index
Publication venue
Publication date
Field of study

Nao informado