Citations: North-Holland - Berge (ResearchIndex)

113 citations found. Retrieving documents...

C. Berge [1985], Graphs, North-Holland, Amsterdam, Chap. 14.

Home/Search Document Not in Database Summary Related Articles Check

This paper is cited in the following contexts:

First 50 documents Next 50

The Chromatic Numbers of Random Hypergraphs - Krivelevich, Sudakov (1998) (1 citation) (Correct)

....H is an ordered pair H = V; E) where V is a nite set (the vertex set) and E is a family of distinct subsets of V (the edge set) A hypergraph H = V; E) is r uniform if all edges of H are of size r. In this paper we consider only r uniform hypergraphs. Our terminology follows that of [3]. A random r uniform hypergraph H r (n; p) is an r uniform hypergraph on n labeled vertices V = n] f1; ng, in which every subset e V of size jej = r is chosen to be an edge of H randomly and independently with probability p, where p may depend on n. Thus, for r = 2 this model reduces ....

C. Berge, Hypergraphs, North-Holland, Amsterdam, 1989.

Circuit Bases of Strongly Connected Digraphs - Gleiss, Leydold, al. (2001) (1 citation) (Correct)

....of G(V; A) consisting exclusively of elementary circuits. A cycle basis is a basis of the cycle space C of G(V; A) consisting exclusively of elementary cycles. Lemma 2 raises the question under which conditions the circuits generate the cycle space. This question was essentially answered by Berge [3]: Proposition 6. 3] A strongly connected digraph G(V; A) has a circuit basis. The converse of Prop. 6 is easily obtained: Theorem 7. A digraph G(V; A) has a circuit basis if and only if each block is either strongly connected or a single arc. Proof: The cycle space of G(V; A) is the direct ....

....exclusively of elementary circuits. A cycle basis is a basis of the cycle space C of G(V; A) consisting exclusively of elementary cycles. Lemma 2 raises the question under which conditions the circuits generate the cycle space. This question was essentially answered by Berge [3] Proposition 6. [3] A strongly connected digraph G(V; A) has a circuit basis. The converse of Prop. 6 is easily obtained: Theorem 7. A digraph G(V; A) has a circuit basis if and only if each block is either strongly connected or a single arc. Proof: The cycle space of G(V; A) is the direct sum of the blocks of G. ....

[Article contains additional citation context not shown here]

C. Berge. Graphs. North-Holland, Amsterdam, NL, 1985.

Circuit Bases of Strongly Connected Digraphs - Gleiss, Leydold, al. (2003) (1 citation) (Correct)

....of G(V, A) consisting exclusively of elementary circuits. A cycle basis is a basis of the cycle space C of G(V, A) consisting exclusively of elementary cycles. Lemma 2 raises the question under which conditions the circuits generate the cycle space. This question was essentially answered by Berge [3]: Proposition 6. 3] A strongly connected digraph G(V, A) has a circuit basis. The converse of Prop. 6 is easily obtained: Theorem 7. A digraph G(V, A) has a circuit basis if and only if each block is either strongly connected or a single arc. Proof. The cycle space of G(V, A) is the direct ....

....exclusively of elementary circuits. A cycle basis is a basis of the cycle space C of G(V, A) consisting exclusively of elementary cycles. Lemma 2 raises the question under which conditions the circuits generate the cycle space. This question was essentially answered by Berge [3] Proposition 6. [3] A strongly connected digraph G(V, A) has a circuit basis. The converse of Prop. 6 is easily obtained: Theorem 7. A digraph G(V, A) has a circuit basis if and only if each block is either strongly connected or a single arc. Proof. The cycle space of G(V, A) is the direct sum of the blocks of G. ....

[Article contains additional citation context not shown here]

C. Berge. Graphs. North-Holland, Amsterdam, NL, 1985.

Connected Morphological Operators for Binary Images - Heijmans (1999) (6 citations) (Correct)

....is not a strong connectivity) and as a result also the zonal graph associated with an image X consists of two disjoint parts. For 4 and 8 adjacency the zonal graph is always connected. In fact, a much stronger result holds in the case of 8 adjacency. Recall that a tree is a graph without cycles [2]. 6.3. Proposition. Consider the connectivity on Z given by 8 adjacency. If X Z , then the graph (P (X) is a tree. A proof has been given by Kong and Roscoe [18] The example in Figure 6.3 shows that this result is not valid in the 4 adjacent case. 14 B C B A A B A A B A B ....

Berge, C. Graphs, 2nd ed. North-Holland, Amsterdam, 1985.

Distance Approximating Trees for Chordal and Dually.. - Brandstädt, Chepoi.. (1997) (5 citations) (Correct)

....we show that the procedure from the previous section can be applied to produce multiplicative 4 spanners and additive 3 spanners in dually chordal graphs, another generalization of strongly chordal graphs. To define dually chordal graphs, we need some notions from the theory of hypergraphs [1]. Let E be a hypergraph with underlying set V; i.e. E is a collection of subsets of V: The dual hypergraph E has E as its vertex set and for every v 2 V a hyperedge fe 2 E : v 2 e.g. The line graph L(E) E ; E) of E is the intersection graph of E , i.e. ee 2 E if and only if e e 6= ....

C. Berge, Hypergraphs, North Holland, Amsterdam, 1989.

Multirelational Semantics for Extended Entity-Relationship.. - Vigna (Correct)

....However, it is easy to see that this test is not sufficient: consider a situation in which the entity type E owns W , F is an E and W owns F . In this case there is no cycle, but an entity of type F could own itself through W . 4. 1 The Algorithm We start with two definitions from graph theory [Ber85]: Definition 3 A path is simple if it does not contain the same node twice, unless it is the first and the last node of the path. Two paths of a graph are said to be parallel if they start on the same node and end on the same node. The problem in analyzing statically ownership is that WEAK ....

Claude Berge. Graphs. North--Holland, Amsterdam, 1985.

On-Line Routing and Wavelength Assignment for.. - Saengudomlert.. (2003) (Correct)

....matching assigned to directed wavelength # 1 simply as the bipartite matching of # 1 . Figure 7c shows example bipartite matchings of specific directed wavelengths. Note that there are at most C sessions in each matching. We next state a known useful lemma related to bipartite graphs (e.g. [19]) node degree m, we can color the edges inE so that no two adjacent edges have the same color using m colors. Consider coloring the edges in a bipartite graph (V 1 , as suggested by lemma 6. Since no two adjacent edges have the same color, the edges with the same color form a ....

C. Berge, Graphs. North-Holland, 1985.

Neural Network Design for Switching Network Control - Brown (1991) (2 citations) (Correct)

....sets is 2 Nn 4.3 . In the case of the non blocking switch, the problem of finding a maximal non blocking set of cells to send reduces to the cardinality graph matching problem. This latter problem has a known polynomial time algorithm that solves it exactly [18] Given a bipartite graph [19], a set M of edges is a matching if no two edges in M are incident to the same node. The cardinality matching problem is to find 79 Figure 4.6: Average queue size vs. average number arrivals for simulations of Bernoulli tra#c into Banyan (a) and non blocking (b) switches with 2 to 32 inputs. 80 ....

Berge, C., Graphs, North-Holland, Amsterdam, 1985, p. 129. 97

On Conflict-Free Coloring of Points and Simple Regions in.. - Har-Peled, Smorodinsky (Correct)

....hypergraph H on V consists of V together with a set E of subsets of V of size k (those are the hyper edges of H) The degree of a vertex v V is the number of sets (i.e. hyper edges) of E that contain v. A set A V is called an independent set if no hyper edge of E is contained in A. See [3] for more details concerning uniform hypergraphs. Lemma 2.5 (i) Let G be a simple graph on n vertices with average degree #. Then G contains an independent set of n #) ii) Let H be a k uniform hypergraph with n vertices and average degree #. Then H contains an independent set of . ....

C. Berge. Hypergraphs. North Holland, Amsterdam, 1989.

Combinatorial Games: Selected Bibliography with a Succinct.. - Fraenkel (2006) (2 citations) (Correct)

No context found.

C. Berge [1985], Graphs, North-Holland, Amsterdam, Chap. 14.

On Hidden Groups in Communication Networks - Baumes, Goldberg.. (2005) (Correct)

No context found.

C. Berge. Hypergraphs. North-Holland, New York, 1978.

Discovering Hidden Groups in Communication Networks - Baumes, Goldberg.. (2004) (Correct)

No context found.

Berge, C.: Hypergraphs. North-Holland, New York (1978)

Wavelength Assignment Algorithms for WDM Optical Networks - Bian (2003) (Correct)

No context found.

Claude Berge. Graphs. North Holland, 1985.

Efficient Collective Communication in Optical Networks - Bermond, Gargano.. (35 citations) (Correct)

No context found.

C. Berge, Graphs, North--Holland.

Collective Tree Spanners of Graphs - Dragan, Yan, Lomonosov (2004) (Correct)

No context found.

C. Berge, Hypergraphs, North Holland, 1989.