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The formalization of simple graphs
 Journal of Formalized Mathematics
, 1994
"... Summary. A graph is simple when • it is nondirected, • there is at most one edge between two vertices, • there is no loop of length one. A formalization of simple graphs is given from scratch. There is already an article [10], dealing with the similar subject. It is not used as a startingpoint, be ..."
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Cited by 21 (0 self)
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Summary. A graph is simple when • it is nondirected, • there is at most one edge between two vertices, • there is no loop of length one. A formalization of simple graphs is given from scratch. There is already an article [10], dealing with the similar subject. It is not used as a starting
On Equational Simple Graphs
, 1997
"... We consider simple graphs that can be obtained from the infinite complete binary tree B by some simple languagetheoretic operations. Their decision problems for sentences in monadic secondorder logic are reduced to those of B in a straightforward manner and therefore are solvable by the famous res ..."
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Cited by 13 (1 self)
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We consider simple graphs that can be obtained from the infinite complete binary tree B by some simple languagetheoretic operations. Their decision problems for sentences in monadic secondorder logic are reduced to those of B in a straightforward manner and therefore are solvable by the famous
An index formula for simple graphs
, 2012
"... Abstract. We prove that any odd dimensional geometric graph G = (V, E) has zero curvature everywhere. To do so, we prove that for every injective function f on the vertex set V of a simple graph the index formula 1 [1 − 2 χ(S(x))/2 − χ(Bf (x))] = (if (x) + i−f (x))/2 = jf (x) holds, where if (x) is ..."
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Cited by 7 (7 self)
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Abstract. We prove that any odd dimensional geometric graph G = (V, E) has zero curvature everywhere. To do so, we prove that for every injective function f on the vertex set V of a simple graph the index formula 1 [1 − 2 χ(S(x))/2 − χ(Bf (x))] = (if (x) + i−f (x))/2 = jf (x) holds, where if (x
On fcolorings of simple graphs
"... Let G be a graph and let f be a function which assigns a positive integer f(v) to each vertex v ∈ V (G). An fcoloring of G is an edgecoloring such that ..."
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Let G be a graph and let f be a function which assigns a positive integer f(v) to each vertex v ∈ V (G). An fcoloring of G is an edgecoloring such that
Books in graphs
, 2008
"... A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α) ..."
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Cited by 2380 (22 self)
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A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α
Simple Graph Editing
"... Applications of mathematics occasionally produce models that are best understood and visualized as directed or undirected graphs. Computer aids to mathematicians can contribute to the understanding and communication of this information, especially if wellintegrated into the problemsolving working ..."
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Applications of mathematics occasionally produce models that are best understood and visualized as directed or undirected graphs. Computer aids to mathematicians can contribute to the understanding and communication of this information, especially if wellintegrated into the problemsolving working
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
Results 1  10
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885,270