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8 research outputs found

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 $BR_m(H_1,H_2)$

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

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

The bipartite Ramsey numbers $BR(C_8, C_{2n})$

Author: Gholami Mostafa
Rowshan Yaser
Yaser Rowshan
Mostafa Gholami
Publication venue
Publication date: 03/01/2024
Field of study

For the given bipartite graphs

G_1,G_2,\ldots,G_t

, the multicolor bipartite Ramsey number

BR(G_1,G_2,\ldots,G_t)

is the smallest positive integer

b

such that any

t

-edge-coloring of

K_{b,b}

contains a monochromatic subgraph isomorphic to

G_i

, colored with the

i

th color for some

1\leq i\leq t

. We compute the exact values of the bipartite Ramsey numbers

BR(C_8,C_{2n})

for

n\geq2

arXiv.org e-Print Archive

Episciences.org

Directory of Open Access Journals

The Size, Multipartite Ramsey Numbers for nK2 Versus Path–Path and Cycle

Author: Stanford Shateyi
Yaser Rowshan
Mostafa Gholami
Publication venue
Publication date: 01/04/2021
Field of study

For given graphs G1,G2,…,Gn and any integer j, the size of the multipartite Ramsey number mj(G1,G2,…,Gn) is the smallest positive integer t such that any n-coloring of the edges of Kj×t contains a monochromatic copy of Gi in color i for some i, 1≤i≤n, where Kj×t denotes the complete multipartite graph having j classes with t vertices per each class. In this paper, we computed the size of the multipartite Ramsey numbers mj(K1,2,P4,nK2) for any j,n≥2 and mj(nK2,C7), for any j≤4 and n≥2

Multidisciplinary Digital Publishing Institute

A Proof of a Conjecture on Bipartite Ramsey Numbers B(2,2,3)

Author: Stanford Shateyi
Yaser Rowshan
Mostafa Gholami
Publication venue
Publication date: 23/02/2022
Field of study

The bipartite Ramsey number B(n1,n2,…,nt) is the least positive integer b, such that any coloring of the edges of Kb,b with t colors will result in a monochromatic copy of Kni,ni in the i-th color, for some i, 1≤i≤t. The values B(2,5)=17, B(2,2,2,2)=19 and B(2,2,2)=11 have been computed in several previously published papers. In this paper, we obtain the exact values of the bipartite Ramsey number B(2,2,3). In particular, we prove the conjecture on B(2,2,3) which was proposed in 2015—in fact, we prove that B(2,2,3)=17

Multidisciplinary Digital Publishing Institute

Directory of Open Access Journals

Exploring the Dimensions and Components of Islamic Values Influencing the Productivity of Human Resources from the Perspective of Mashhad Municipality Employees

Author: Rowshan Seyed Aligholi
Nejad Afagh Arjmandi
Yaghoubi Noor Mohammad
Doaei Habibollah
Publication venue
Publication date: 12/09/2016
Field of study

AbstractThe present study was performed to explore the components and dimensions of Islamic values affecting the productivity of human resources from the perspective of Mashhad Municipality employees using a hybrid method. For this purpose, in-depth interviews were performed with 20 administrative and scientific experts of Mashhad Municipality using content analysis. The results obtained from semi-structured interviews were classified into the dimensions of non-promotion of religious and revolutionary values, not spending enough on culture-building, approving the wrongdoer in the system, lack of suitable role model and creating substrates for anti-values as the factors affecting Islamic values; each of these behaviors consist of other concepts. The dimensions along with the components of Islamic values questionnaire including piety, tolerance and trust were examined in a sample of 215 employees in 13 Mashhad Municipality zones. In fact, the findings of this study expand the area in the field of organizational studies by providing dimensions and components of human resources productivity from the employees’ perspectives and increase human resources productivity in organizations. The results of this study are consistent with some of the most important domestic and foreign research on different aspects of productivity (Katcher (1991); Shaser (1983), Goodwin (2007); Kesty (2012), etc.)

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