scholarly journals A note on the weak splitting number

2020 ◽  
pp. 1
Author(s):  
Alberto Cavallo ◽  
Carlo Collari ◽  
Anthony Conway
Keyword(s):  
Splitting Number

scholarly journals Connected Numbers and the Embedded Topology of Plane Curves

2018 ◽  
Vol 61 (3) ◽  
pp. 650-658 ◽  
Author(s):  
Taketo Shirane
Keyword(s):  
Plane Curve ◽  
Smooth Curve ◽  
Plane Curves ◽  
Irreducible Curve ◽  
Galois Cover ◽  
Splitting Number

AbstractThe splitting number of a plane irreducible curve for a Galois cover is effective in distinguishing the embedded topology of plane curves. In this paper, we define the connected number of a plane curve (possibly reducible) for a Galois cover, which is similar to the splitting number. By using the connected number, we distinguish the embedded topology of Artal arrangements of degree b ≥ 4, where an Artal arrangement of degree b is a plane curve consisting of one smooth curve of degree b and three of its total inflectional tangents.

Splitting Number is NP-Complete

1998 ◽  
pp. 285-297 ◽  
Author(s):  
L. Faria ◽  
C. M. H. de Figueiredo ◽  
C. F. X. Mendonça
Keyword(s):  
Splitting Number ◽  
Np Complete

scholarly journals On the cofinality of the splitting number

2018 ◽  
Vol 29 (1) ◽  
pp. 382-395 ◽  
Author(s):  
Alan Dow ◽  
Saharon Shelah
Keyword(s):  
Splitting Number

The splitting number of complete bipartite graphs

1984 ◽  
Vol 42 (2) ◽  
pp. 178-184 ◽  
Author(s):  
B. Jackson ◽  
G. Ringel
Keyword(s):  
Bipartite Graphs ◽  
Splitting Number ◽  
Complete Bipartite Graphs

Splitting number at uncountable cardinals

1997 ◽  
Vol 62 (1) ◽  
pp. 35-42 ◽  
Author(s):  
Jindřich Zapletal
Keyword(s):  
Large Cardinal ◽  
Inner Models ◽  
Splitting Number ◽  
Uncountable Cardinal ◽  
Uncountable Cardinals

AbstractWe study a generalization of the splitting number s to uncountable cardinals. We prove that 𝔰(κ) > κ+ for a regular uncountable cardinal κ implies the existence of inner models with measurables of high Mitchell order. We prove that the assumption 𝔰(ℵω) > ℵω+1 has a considerable large cardinal strength as well.

The splitting number of the complete graph

1985 ◽  
Vol 1 (1) ◽  
pp. 311-329 ◽  
Author(s):  
Nora Hartsfield ◽  
Brad Jackson ◽  
Gerhard Ringel
Keyword(s):  
Complete Graph ◽  
Splitting Number

scholarly journals Shuffled Frog Leaping Algorithm for Preemptive Project Scheduling Problems with Resource Vacations Based on Patterson Set

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Yi Han ◽  
Ikou Kaku ◽  
Jianhu Cai ◽  
Yanlai Li ◽  
Chao Yang ◽  
...  
Keyword(s):  
Project Scheduling ◽  
Single Mode ◽  
Medium Size ◽  
Scheduling Problems ◽  
Shuffled Frog Leaping Algorithm ◽  
Scarce Resources ◽  
Splitting Number ◽  
Shuffled Frog Leaping ◽  
Project Scheduling Problem ◽  
Effectiveness And Efficiency

This paper presents a shuffled frog leaping algorithm (SFLA) for the single-mode resource-constrained project scheduling problem where activities can be divided into equant units and interrupted during processing. Each activity consumes 0–3 types of resources which are renewable and temporarily not available due to resource vacations in each period. The presence of scarce resources and precedence relations between activities makes project scheduling a difficult and important task in project management. A recent popular metaheuristic shuffled frog leaping algorithm, which is enlightened by the predatory habit of frog group in a small pond, is adopted to investigate the project makespan improvement on Patterson benchmark sets which is composed of different small and medium size projects. Computational results demonstrate the effectiveness and efficiency of SFLA in reducing project makespan and minimizing activity splitting number within an average CPU runtime, 0.521 second. This paper exposes all the scheduling sequences for each project and shows that of the 23 best known solutions have been improved.

scholarly journals splitting number is NP-complete

2001 ◽  
Vol 108 (1-2) ◽  
pp. 65-83 ◽  
Author(s):  
L. Faria ◽  
C.M.H. de Figueiredo ◽  
C.F.X. Mendonça
Keyword(s):  
Splitting Number ◽  
Np Complete

scholarly journals Splitting number

1997 ◽  
Vol 125 (7) ◽  
pp. 2141-2145 ◽  
Author(s):  
Tomek Bartoszynski
Keyword(s):  
Splitting Number
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