Compatible Euler Tours In Eulerian Digraphs

1990 ◽  
pp. 95-100 ◽  
Author(s):  
H. Fleischner ◽  
B. Jackson
Keyword(s):  
Euler Tours

Random Sampling of Euler Tours

Algorithmica ◽  
2001 ◽  
Vol 30 (3) ◽  
pp. 376-385 ◽  
Author(s):  
P. Tetali ◽  
S. Vempala
Keyword(s):  
Random Sampling ◽  
Euler Tours

Transformations of Euler Tours

1980 ◽  
pp. 65-69 ◽  
Author(s):  
Jaromir Abrham ◽  
Anton Kotzig
Keyword(s):  
Euler Tours

scholarly journals Finding Euler tours in parallel

1984 ◽  
Vol 29 (3) ◽  
pp. 330-337 ◽  
Author(s):  
Mikhail Atallah ◽  
Uzi Vishkin
Keyword(s):  
Euler Tours

scholarly journals Euler tours and a game with dominoes

1997 ◽  
Vol 167-168 ◽  
pp. 511-517
Author(s):  
Victor Neumann-Lara ◽  
Eduardo Rivera-Campo
Keyword(s):  
Euler Tours

ON FINDING EULER TOURS IN PARALLEL

1993 ◽  
Vol 03 (03) ◽  
pp. 223-231 ◽  
Author(s):  
EDSON N. CACERES ◽  
NARSINGH DEO ◽  
SHIVAKUMAR SASTRY ◽  
JAYME L. SZWARCFITER
Keyword(s):  
Parallel Algorithm ◽  
Spanning Tree ◽  
Intermediate Step ◽  
Euler Tour ◽  
Euler Tours

We describe an alternative implementation of Atallah and Vishkin’s parallel algorithm for finding an Euler Tour of a graph. Instead of finding a spanning tree as an intermediate step, this algorithm is based on identifying a strut which is easier to compute. Using the strut, vertices which have more than one circuit passing through them are identified directly. Stitching at such vertices reduces the number of circuits in the Euler Partition.

scholarly journals Compatible Euler Tours and Supplementary Eulerian Vectors

1993 ◽  
Vol 14 (6) ◽  
pp. 513-520 ◽  
Author(s):  
André Bouchet
Keyword(s):  
Euler Tours

scholarly journals The number of Euler tours of a random $d$-in/$d$-out graph

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Páidí Creed ◽  
Mary Cryan
Keyword(s):  
Asymptotic Distribution ◽  
Directed Graph ◽  
Polynomial Time ◽  
Simple Approach ◽  
Uniform Sampling ◽  
Concentration Result ◽  
International Audience ◽  
De Bruijn ◽  
Euler Tours

International audience In this paper we obtain the expectation and variance of the number of Euler tours of a random $d$-in/$d$-out directed graph, for $d \geq 2$. We use this to obtain the asymptotic distribution and prove a concentration result. We are then able to show that a very simple approach for uniform sampling or approximately counting Euler tours yields algorithms running in expected polynomial time for almost every $d$-in/$d$-out graph. We make use of the BEST theorem of de Bruijn, van Aardenne-Ehrenfest, Smith and Tutte, which shows that the number of Euler tours of a $d$-in/$d$-out graph is the product of the number of arborescences and the term $[(d-1)!]^n/n$. Therefore most of our effort is towards estimating the asymptotic distribution of the number of arborescences of a random $d$-in/$d$-out graph.

scholarly journals Euler Tours a través del software Scratch: una secuencia de tareas de investigación

PARADIGMA ◽  
2020 ◽  
pp. 476-498
Author(s):  
Priscilla Frida Salles Tojeiro ◽  
Eliane Maria de Oliveira Araman
Keyword(s):  
Euler Tours

O presente artigo tem como objetivo apresentar uma sequência de tarefas que foi desenvolvida pelas pesquisadoras bem como os resultados da aplicação desta para alunos do quarto e quinto ano do Ensino Fundamental de uma escola municipal na cidade de Ourinhos, Brasil. Inspirada no problema histórico “As sete pontes de Königsberg”, a sequência compreende nove tarefas que foram desenvolvidas com o software Scratch. Ao tentarem resolver as tarefas, os alunos a fizeram de forma investigativa. A escolha por este problema caracterizou-se por ser de fácil contextualização com a realidade atual e ao ser adaptado ao contexto infantil, permitiu que os alunos percebessem uma utilização prática de conhecimentos aprendidos em sala de aula como: movimentação de objeto no espaço plano, estudo de vértices, arestas, números pares e ímpares, conhecimentos previstos como conteúdos dos Anos Iniciais do Ensino Fundamental. A metodologia adotada foi de natureza qualitativa. Os resultamos mostraram que os alunos conseguiram aproximarem-se dos quatro teoremas, alguns com desempenho melhor que outros. As tarefas permitiram que se expressassem oralmente e por meio de escrita, o que possibilitou reflexões sobre o objeto de estudo por parte dos alunos e das pesquisadoras.

Trees and Euler Tours in a Planar Graph and Its Relatives

1987 ◽  
Vol 94 (7) ◽  
pp. 618-630 ◽  
Author(s):  
Mark E. Kidwell ◽  
R. Bruce Richter
Keyword(s):  
Planar Graph ◽  
Euler Tours
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