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Ciclos Eulerianos y Hamiltonianos

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Ciclos Eulerianos y Hamiltonianos

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Quiz sobre ciclos y caminos

Created by

Emily Cárdenas
Emily Cárdenas
Ecuador

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Ciclos Eulerianos y Hamiltonianos
 

Ciclos Eulerianos y HamiltonianosOnline version

Quiz sobre ciclos y caminos

by Emily Cárdenas
1

¿Qué es un ciclo euleriano en un grafo no dirigido?

2

¿Qué define a un ciclo hamiltoniano?

3

Condición necesaria para que exista un ciclo euleriano en un grafo no dirigido?

4

Si exactamente dos vértices tienen grado impar, ¿qué puede existir?

5

Diferencia clave entre Hamiltoniano y Euleriano?

6

¿Es posible que un grafo tenga un camino Hamiltoniano pero no un ciclo Hamiltoniano?

7

¿Qué problema de complejidad está asociado al ciclo hamiltoniano?

8

En un grafo conexo, si todos los vértices tienen grado par, ¿qué se garantiza?

9

Segunda condición típica de Dirac para Hamiltonianos?

10

¿Puede haber grafos Eulerianos que no tengan un Hamiltoniano?

Explicación

Explica que se exige cubrir cada arista una sola vez.

Se centra en vértices, no en aristas.

En grafos conexos, grado par en todos los vértices garantiza ciclo euleriano.

Con dos grados impares, solo hay trazo que usa cada arista exactamente una vez.

Hamiltoniano se refiere a visitar vértices; Euleriano a aristas.

Un Hamiltoniano puede existir sin formar un ciclo al terminar.

Encontrar Hamiltonianos es un problema NP-completo conocido.

Propiedad suficiente para un ciclo que recorre todas las aristas.

Dirac da una cota suficiente para Hamiltoniano.

La existencia de un ciclo euleriano no implica un Hamiltoniano.

 
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