An example of an ear decomposition of a graph containing 3 ears.
In graph theory, an ear of an undirected graph G is a path P where the two endpoints of the path may coincide, but where otherwise no repetition of edges or vertices is allowed, so every internal vertex of P has degree two in G. An ear decomposition of an undirected graph G is a partition of its set of edges into a sequence of ears, such that the one or two endpoints of each ear belong to earlier ears in the sequence and such that the internal vertices of each ear do not belong to any earlier ear. Additionally, in most cases the first ear in the sequence must be a cycle. An open ear decomposition or a proper ear decomposition is an ear decomposition in which the two endpoints of each ear after the first are distinct from each other.
Ear decompositions may be used to characterize several important graph classes, and as part of efficient graph algorithms. They may also be generalized from graphs to matroids.
whose first appearance in the decomposition is in a later ear than the first appearance of v. This type of eardecomposition may be used to generalize Whitney's...
particular Theorems 18 (relating eardecomposition to circuit rank) and 19 (on the existence of eardecompositions). Brualdi, Richard A. (2006), Combinatorial...
algorithms may be based on eardecomposition. While the DFS-based algorithms above depend inherently on the special open eardecomposition caused by the underlying...
above algorithm uses chain decompositions, which are special eardecompositions depending on DFS-trees. Chain decompositions can be computed in linear...
randomized algorithm with linear expected time is also known. Seidel's decomposition algorithm and Chazelle's triangulation method are discussed in detail...
decomposition may also be found with the additional property that a chosen matroid element belongs to every circuit. Finding a branch-decomposition of...
An otolith (Greek: ὠτο-, ōto- ear + λῐ́θος, líthos, a stone), also called statoconium or otoconium or statolith, is a calcium carbonate structure in the...
farthest from line uw. This diagonal decomposes the polygon into two smaller polygons, and repeated decomposition by ears and diagonals eventually produces...
smaller intervals. Consequently, in this context the above-mentioned "decomposition" of the tritone into six semitones is typically not allowed. If a diatonic...
They were also extended to the more general notion of non-separating eardecompositions. In some algorithms for testing planarity of graphs, it is useful...
Fusarium ear blight (FEB) (also called Fusarium head blight, FHB, or scab), is a fungal disease of cereals, including wheat, barley, oats, rye and triticale...
Joseph (2005-10-01). "An O ( V E ) {\displaystyle O(VE)} algorithm for eardecompositions of matching-covered graphs". ACM Transactions on Algorithms. 1 (2):...
ear. The outer ear consists of the pinna and the ear canal. Since the outer ear is the only visible portion of the ear in most animals, the word "ear"...
opaque secretion that gains its characteristic odor upon bacterial decomposition. Eccrine glands on their paws increase friction and prevent them from...
happens around the second week of decomposition. Gas accumulation and bloating will continue until the body is decomposed sufficiently for the gas to escape...
attribute: their auditory bullae (bony capsules enclosing the middle and inner ear). This is a key diagnostic in classifying species as feliform versus caniform...
body had not decomposed at all or to interpret signs of decomposition as signs of continued life. Corpses swell as gases from decomposition accumulate in...
mutilations, various explanations have been offered, ranging from natural decomposition and normal predation to cults and secretive governmental and military...
and determines if the hypergraph is α-acyclic. If so, it computes a decomposition of the hypergraph. The algorithm was proposed in 1979 by Graham and...
the ears, face, trunk, or extremities, sometimes needing reconstructive surgery. Levamisole is purportedly a common cutting agent. Decomposition of blood...
Fight 2: Mandy Moore is stabbed in the ears with her sharpened lollipop. Her brains are then blown through her ear and spilled on the mat of the ring causing...
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