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Can a graph have an Euler circuit but not a Hamiltonian circuit?
Yes. An example: _____A---------B________ A connected directly to B and D by one path. _____|_______/|\________ B connected directly to A and E by one path, and to C by two paths. _____|______/_|_\_______ _____|_____/___\_|______ _____|__E/_____\|______ E connected directly to B and D by one path. _____|____\_____C______ C connected directly to B and D by two paths. _____|_____\____|\_____ _____|______\___|__\___ _____|_______\__|__/___ _____|________\_|_/____ _____|_________\|/_____ _____-------------D_____ D connected directly to A and E by one path, and to C by two paths. There is an Euler circuit: ABCDEBCDA But a Hamiltonian circuit is impossible: as part of a circuit A can only be reached by the path BAD, but once BAD has been traversed it is impossible to get to both C and E without returning to B or D first. However there is a Hamiltonian Path: ABCDE.
What is the difference between a base path and a base line?
A base path is the path determined by the runner as he is travelling between bases, and the base line is the the direct lines between the two bases.
What is the difference between path and absolute path?
absolute path is an exact road to go in and path is just a relative path, for example the path is near the river - for a path and for an absolute path you can say the path is on green lake street on the intersection of green lake street and Burnside street.
Why will a tapered cup roll in a circular path?
Because there is a difference between the circumferences of the top lip and the base of the cup.
What is the difference between a polygon and a polyhedron?
polyhedron is often defined as a geometric object with flat faces and straight edges polygon is traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). .
