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In graph-theoretic terminology, the four-color theorem states that the vertices of every planar graph can be colored with at most four colors so that no two adjacent vertices receive the same color, or for short, " every planar graph is four-colorable " (; ).
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graph-theoretic and theorem
Dunwoody found a graph-theoretic proof of Stallings ' theorem about ends of groups in 1982, by constructing certain tree-like automorphism invariant graph decompositions.
Every comparability graph is perfect: this is essentially just Mirsky's theorem, restated in graph-theoretic terms.
Therefore, the complement of any comparability graph is perfect ; this is essentially just Dilworth's theorem itself, restated in graph-theoretic terms.
graph-theoretic and every
The transitive closure of G has an edge u → v for every related pair u ≤ v of distinct elements in the reachability relation of G, and may therefore be thought of as a direct translation of the reachability relation ≤ into graph-theoretic terms: every partially ordered set may be translated into a DAG in this way.
An alternative model considers a spring-like force for every pair of nodes where the ideal length of each spring is proportional to the graph-theoretic distance between nodes i and j.
graph-theoretic and planar
In more formal graph-theoretic terms, the problem asks whether the complete bipartite graph K < sub > 3, 3 </ sub > is planar.
graph-theoretic and graph
The introduction of probabilistic methods in graph theory, especially in the study of Erdős and Rényi of the asymptotic probability of graph connectivity, gave rise to yet another branch, known as random graph theory, which has been a fruitful source of graph-theoretic results.
However, it has two graph-theoretic interpretations: as the sum of weights of cycle covers of a directed graph, and as the sum of weights of perfect matchings in a bipartite graph.
If the edges of a graph are thought of as lines drawn from one vertex to another ( as they are usually depicted in illustrations ), then two graphs are homeomorphic to each other in the graph-theoretic sense precisely if they are homeomorphic in the sense in which the term is used in topology.
* A leaf vertex in graph theory, of degree 1 in a graph-theoretic tree
* For the graph-theoretic concept, see connected component ( graph theory ).
In graph-theoretic mathematics, the circuit rank or cyclomatic number of an undirected graph is the minimum number of edges to remove from to remove all its cycles, making it into a forest.
He worked mainly in graph theory, and is known for introducing a graph-theoretic view of pursuit-evasion problems ( Parsons 1976, 1978 ).
Contributions for which Luce is known include formulating Luce's choice axiom formalizing the principle that additional options should not affect the probability of selecting one item over another, defining semiorders, introducing graph-theoretic methods into the social sciences, and coining the term " clique " for a complete subgraph in graph theory.
graph-theoretic and can
In condensed matter physics, the three dimensional structure of complicated simulated atomic structures can be studied quantitatively by gathering statistics on graph-theoretic properties related to the topology of the atoms.
graph-theoretic and be
These problems may be analyzed using graph-theoretic methods, by dynamic programming, or by integer programming.
graph-theoretic and with
New graph-theoretic algorithms were invented by Lederberg, Harold Brown, and others that generate all graphs with a specified set of nodes and connection-types ( chemical atoms and bonds ) -- with or without cycles.
graph-theoretic and at
Although the study of complete subgraphs goes back at least to the graph-theoretic reformulation of Ramsey theory by, the term " clique " comes from, who used complete subgraphs in social networks to model cliques of people ; that is, groups of people all of whom know each other.
Indeed it is not a tree at all in the graph-theoretic sense, because it contains parallel edges.
graph-theoretic and is
It is convenient to phrase the problem in graph-theoretic language.
terminology and theorem
In mathematics terminology, the vector space of bras is the dual space to the vector space of kets, and corresponding bras and kets are related by the Riesz representation theorem.
The proof of Gödel's completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 ( and a rewritten version of the dissertation, published as an article in 1930 ) is not easy to read today ; it uses concepts and formalism that are outdated and terminology that is often obscure.
Bayes ' theorem was named after the Reverend Thomas Bayes ( 1702 – 61 ), who studied how to compute a distribution for the probability parameter of a binomial distribution ( in modern terminology ).
The terminology is confused, since the result is also called the Noether – Enriques theorem.
terminology and states
Andreas Köstenberger states that the fact that the 10th century Arabic version of the Testimonium ( discovered in the 1970s ) lacks distinct Christian terminology while sharing the essential elements of the passage indicates that the Greek Testimonium has been subject to interpolation.
In states with a more mature system, the set of Conflict rules stands apart from the local private civil law and adopts a more international point of view both in its terminology and concepts.
Article 95 introduces the terminology " quadratic residue " and " quadratic nonresidue ", and states that, if the context makes it clear, the adjective " quadratic " may be dropped.
The terminology varies among ( and sometimes within ) the several states.
Imperial states that have used this terminology include Ancient Rome, the Mongol Empire, and the British Empire.
It states that any deterministic dynamic system will automatically evolve towards a state of equilibrium ( or in more modern terminology, an attractor ).
Vita B states that Callimachus was his instructor in rhetoric (), but the terminology is anachronistic.
Despite this difference in terminology, however, the heads of government of these city-states hold the same power and position as the ministers-president of the other German states.
In the weeks following the 2000 election, however, there arose the terminology of red states and blue states, in which the conservative Republican Party was associated with red and the liberal Democratic Party with blue.
According to The Washington Post, the phrases red states and blue states were coined by Tim Russert, although in that same article Russert states that he wasn't the first to use the terminology.
The summons is called a " subpoena for production of evidence " in some U. S. states that have sought to reduce the use of non-English words and phrases in court terminology.
In this context, one does not usually use Fourier terminology and instead one states that f ( x ) is the characteristic function of a symmetric PDF.
In this work he states his reasons for requiring a new method and new terminology.
In Marxist terminology, wars of national liberation or national liberation revolutions are conflicts fought by oppressed nationalities against imperial powers to establish separate sovereign states for the subjugated nationality.
A cladogram showing the terminology used to describe different patterns of ancestral and derived character states.
: Although they did not use the terminology of the Gnostics, nor did they probably even know of them, their use of the words ' knowledge ' and ' ignorance ' as different states of spiritual awareness are strikingly reminiscent of the earlier movement as they are of the terminology of other religions and mystical movements such as Buddhism and Sufism.
Much more serious was the problem of elements which form more than one oxide or series of salts, which have ( in today's terminology ) different oxidation states.
2.650 seconds.