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Anything inside the path will be included after the clipping path is applied; anything outside the path will be omitted from the output. Applying the clipping path results in a hard (aliased) or soft (anti-aliased) edge, depending on the image editor's capabilities. Clipping path. By convention, the inside of the path is defined by its direction.
A path such that no graph edges connect two nonconsecutive path vertices is called an induced path. A path that includes every vertex of the graph without repeats is known as a Hamiltonian path. Two paths are vertex-independent (alternatively, internally disjoint or internally vertex-disjoint) if they do not have any internal vertex or edge in ...
Given a matching M, an alternating path is a path that begins with an unmatched vertex [3] and whose edges belong alternately to the matching and not to the matching. An augmenting path is an alternating path that starts from and ends on free (unmatched) vertices.
Shortest path (A, C, E, D, F), blue, between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
The property of having pathwidth at most p is, itself, closed under taking minors: if G has a path-decomposition with width at most p, then the same path-decomposition remains valid if any edge is removed from G, and any vertex can be removed from G and from its path-decomposition without increasing the width. Contraction of an edge, also, can ...
The Herschel graph is the smallest possible polyhedral graph that does not have a Hamiltonian cycle. A possible Hamiltonian path is shown. Any Hamiltonian cycle can be converted to a Hamiltonian path by removing one of its edges, but a Hamiltonian path can be extended to a Hamiltonian cycle only if its endpoints are adjacent.
In a graph with a matching, an alternating path is a path whose edges alternate between matched and unmatched edges. An alternating cycle is, similarly, a cycle whose edges alternate between matched and unmatched edges. An augmenting path is an alternating path that starts and ends at unsaturated vertices.
A central problem in algorithmic graph theory is the shortest path problem.One of the generalizations of the shortest path problem is known as the single-source-shortest-paths (SSSP) problem, which consists of finding the shortest paths from a source vertex to all other vertices in the graph.