scholarly journals On total coloring the direct product of complete graphs

2021 ◽  
Vol 195 ◽  
pp. 306-314
Author(s):  
D. Castonguay ◽  
C.M.H. de Figueiredo ◽  
L.A.B. Kowada ◽  
C.S.R. Patrão ◽  
D. Sasaki ◽  
...  
Keyword(s):  
Direct Product ◽  
Total Coloring ◽  
Complete Graphs

Equitable Total Coloring of Direct Product of Path and Cycle

2019 ◽  
Vol 10 (7) ◽  
pp. 1476-1481
Author(s):  
S. Moidheen Aliyar ◽  
S. Manimaran ◽  
K. Manikandan
Keyword(s):  
Direct Product ◽  
Total Coloring

Distances in Random Induced Subgraphs of Generalized n-Cubes

2002 ◽  
Vol 11 (6) ◽  
pp. 599-605 ◽  
Author(s):  
C. M. REIDYS
Keyword(s):  
Direct Product ◽  
Finite Alphabet ◽  
Complete Graphs ◽  
Induced Subgraphs ◽  
Induced Subgraph ◽  
Random Subgraphs ◽  
Independent Probability

In this paper we study distances in random subgraphs of a generalized n-cube [Qscr ]ns over a finite alphabet S of size s. [Qscr ]ns is the direct product of complete graphs over s vertices, its vertices being the n-tuples (x1, …, xn), with xi ∈ S, i = 1, … n, and two vertices being adjacent if they differ in exactly one coordinate. A random (induced) subgraph γ of [Qscr ]ns is obtained by selecting [Qscr ]ns-vertices with independent probability pn and then inducing the corresponding edges from [Qscr ]ns. Our main result is that dγ (P,Q) [les ] [2k+3]d[Qscr ]ns (P,Q) almost surely for P,Q ∈ γ, pn = n−a and 0 [les ] a < ½, where k = [1+3a/1−2a] and dγ and d[Qscr ]ns denote the distances in γ and [Qscr ]ns, respectively.

scholarly journals ON PLANARITY OF DIRECT PRODUCT OF MULTIPARTITE COMPLETE GRAPHS

2009 ◽  
Vol 01 (01) ◽  
pp. 85-104 ◽  
Author(s):  
LAURENT BEAUDOU ◽  
PAUL DORBEC ◽  
SYLVAIN GRAVIER ◽  
PRANAVA K. JHA
Keyword(s):  
Direct Product ◽  
Complete Graphs ◽  
The Past

The planarity of the direct product of two graphs has been widely studied in the past. Surprisingly, the missing part is the product with K2, which seems to be less predictible. In this piece of work, we characterize which subdivisions of multipartite complete graphs, have their direct product with K2 planar. This can be seen as a step towards the characterization of all such graphs.

scholarly journals Product Dimension of Forests and Bounded Treewidth Graphs

10.37236/2698 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
L. Sunil Chandran ◽  
Rogers Mathew ◽  
Deepak Rajendraprasad ◽  
Roohani Sharma
Keyword(s):  
Natural Number ◽  
Direct Product ◽  
Upper Bound ◽  
Latin Squares ◽  
Complete Graphs ◽  
Induced Subgraph ◽  
Orthogonal Latin Squares ◽  
Bounded Treewidth ◽  
Product Dimension

The product dimension of a graph $G$ is defined as the minimum natural number $l$ such that $G$ is an induced subgraph of a direct product of $l$ complete graphs. In this paper we study the product dimension of forests, bounded treewidth graphs and $k$-degenerate graphs. We show that every forest on $n$ vertices has product dimension at most $1.441 \log n + 3$. This improves the best known upper bound of $3 \log n$ for the same due to Poljak and Pultr. The technique used in arriving at the above bound is extended and combined with a well-known result on the existence of orthogonal Latin squares to show that every graph on $n$ vertices with treewidth at most $t$ has product dimension at most $(t+2)(\log n + 1)$. We also show that every $k$-degenerate graph on $n$ vertices has product dimension at most $\lceil 5.545 k \log n \rceil + 1$. This improves the upper bound of  $32 k \log n$ for the same by Eaton and  Rődl.

Roulette Wheel Selection based Heuristic Algorithm for the Orienteering Problem

2014 ◽  
Vol 13 (1) ◽  
pp. 4127-4145
Author(s):  
Madhushi Verma ◽  
Mukul Gupta ◽  
Bijeeta Pal ◽  
Prof. K. K. Shukla
Keyword(s):  
Triangle Inequality ◽  
Time Budget ◽  
Control Point ◽  
Hamiltonian Path ◽  
Real Life ◽  
Tourism Industry ◽  
Orienteering Problem ◽  
Complete Graphs ◽  
Roulette Wheel Selection ◽  
Roulette Wheel

Orienteering problem (OP) is an NP-Hard graph problem. The nodes of the graph are associated with scores or rewards and the edges with time delays. The goal is to obtain a Hamiltonian path connecting the two necessary check points, i.e. the source and the target along with a set of control points such that the total collected score is maximized within a specified time limit. OP finds application in several fields like logistics, transportation networks, tourism industry, etc. Most of the existing algorithms for OP can only be applied on complete graphs that satisfy the triangle inequality. Real-life scenario does not guarantee that there exists a direct link between all control point pairs or the triangle inequality is satisfied. To provide a more practical solution, we propose a stochastic greedy algorithm (RWS_OP) that uses the roulette wheel selectionmethod, does not require that the triangle inequality condition is satisfied and is capable of handling both complete as well as incomplete graphs. Based on several experiments on standard benchmark data we show that RWS_OP is faster, more efficient in terms of time budget utilization and achieves a better performance in terms of the total collected score ascompared to a recently reported algorithm for incomplete graphs.

Sport and nationalism in the Republic of North Macedonia

Focaal ◽  
2019 ◽  
pp. 1-13
Author(s):  
Vasiliki P. Neofotistos
Keyword(s):  
Direct Product ◽  
Nation Building ◽  
National History ◽  
Sports Teams ◽  
The Balkans ◽  
The North ◽  
Political Forces ◽  
The Republic

Using the Republic of North Macedonia as a case study, this article analyzes the processes through which national sports teams’ losing performance acquires a broad social and political significance. I explore claims to sporting victory as a direct product of political forces in countries located at the bottom of the global hierarchy that participate in a wider system of coercive rule, frequently referred to as empire. I also analyze how public celebrations of claimed sporting victories are intertwined with nation-building efforts, especially toward the global legitimization of a particular version of national history and heritage. The North Macedonia case provides a fruitful lens through which we can better understand unfolding sociopolitical developments, whereby imaginings of the global interlock with local interests and needs, in the Balkans and beyond.

Sign in / Sign up

Export Citation Format

Share Document