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AND INTERVAL GRAPHS
, 1964
"... Approved for public release; distribution is unlimited. Distribution authorized to U.S. Gov't. agencies and their contractors; ..."
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Approved for public release; distribution is unlimited. Distribution authorized to U.S. Gov't. agencies and their contractors;
Counting interval graphs
 Trans. Amer. Math. Soc
, 1982
"... ABSTRACT. In this paper we enumerate interval graphs (up to isomorphism) along with labelled interval graphs, identity interval graphs, transitive interval graphs and various sorts of unit interval graphs. The enumeration makes use of a structural decomposition of interval graphs which leads to a ch ..."
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Cited by 9 (0 self)
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ABSTRACT. In this paper we enumerate interval graphs (up to isomorphism) along with labelled interval graphs, identity interval graphs, transitive interval graphs and various sorts of unit interval graphs. The enumeration makes use of a structural decomposition of interval graphs which leads to a
On homogeneously representable interval graphs
"... We determine all graphs whose line graphs (middle graphs, total graphs, respectively) are homogeneously representable interval graphs. ..."
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We determine all graphs whose line graphs (middle graphs, total graphs, respectively) are homogeneously representable interval graphs.
On Probe Interval Graphs
, 2001
"... In this report, we first studied the characteristics of probe interval graphs. Then we analyzed an O(n³) algorithm, which recongnizes probe interval graphs and gives a possible solution. In addition, the algorithm was illustrated by two examples step by step. Based on our analysis, we provided a des ..."
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Cited by 23 (2 self)
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In this report, we first studied the characteristics of probe interval graphs. Then we analyzed an O(n³) algorithm, which recongnizes probe interval graphs and gives a possible solution. In addition, the algorithm was illustrated by two examples step by step. Based on our analysis, we provided a
Interval graph limits
, 2011
"... We work out the graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function W (x, y) on the unit square, with x and y uniform on the interval (0, 1). Instead, we fix a W and change the underlying distribution of the c ..."
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Cited by 8 (5 self)
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We work out the graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function W (x, y) on the unit square, with x and y uniform on the interval (0, 1). Instead, we fix a W and change the underlying distribution
Tagged Probe Interval Graphs
, 1998
"... A generalization of interval graph is introduced for cosmid contig mapping of DNA. A graph is a tagged probe interval graph if its vertex set can be partitioned into two subsets of probes and nonprobes, and a closed interval can be assigned to each vertex such that two vertices are adjacent if and o ..."
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Cited by 1 (0 self)
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A generalization of interval graph is introduced for cosmid contig mapping of DNA. A graph is a tagged probe interval graph if its vertex set can be partitioned into two subsets of probes and nonprobes, and a closed interval can be assigned to each vertex such that two vertices are adjacent
Characterizations of probe interval graphs
, 2008
"... In this paper we obtain several characterizations of the adjacency matrix of a probe interval graph. In course of this study we describe an easy method of obtaining interval representation of an interval bipartite graph from its adjacency matrix. Finally, we note that if we add a loop at every probe ..."
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In this paper we obtain several characterizations of the adjacency matrix of a probe interval graph. In course of this study we describe an easy method of obtaining interval representation of an interval bipartite graph from its adjacency matrix. Finally, we note that if we add a loop at every
Shiftable Interval Graphs
"... Abstract: A Shiftable Interval Graph (SIG) is defined by a set of intervals and a set of windows associated with the intervals. Each interval does not have a fixed position, but it is allowed to move, provided that it remains completely contained into its window. Once a position has been fixed for a ..."
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Cited by 1 (0 self)
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Abstract: A Shiftable Interval Graph (SIG) is defined by a set of intervals and a set of windows associated with the intervals. Each interval does not have a fixed position, but it is allowed to move, provided that it remains completely contained into its window. Once a position has been fixed
On the Cubicity of Interval Graphs
"... A kcube (or “a unit cube in k dimensions”) is defined as the Cartesian product R1 ×... × Rk where Ri(for 1 ≤ i ≤ k) is an interval of the form [ai, ai + 1] on the real line. The kcube representation of a graph G is a mapping of the vertices of G to kcubes such that the kcubes mapped to two vert ..."
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A kcube (or “a unit cube in k dimensions”) is defined as the Cartesian product R1 ×... × Rk where Ri(for 1 ≤ i ≤ k) is an interval of the form [ai, ai + 1] on the real line. The kcube representation of a graph G is a mapping of the vertices of G to kcubes such that the kcubes mapped to two
kGap interval graphs
 IN: PROC. OF THE 10TH LATIN AMERICAN THEORETICAL INFORMATICS SYMPOSIUM (LATIN) (2012). AVAILABLE AT: ARXIV:1112.3244
, 2012
"... We initiate the study of a new parameterization of graph problems. In a multiple interval representation of a graph, each vertex is associated to at least one interval of the real line, with an edge between two vertices if and only if an interval associated to one vertex has a nonempty intersectio ..."
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Cited by 1 (0 self)
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We initiate the study of a new parameterization of graph problems. In a multiple interval representation of a graph, each vertex is associated to at least one interval of the real line, with an edge between two vertices if and only if an interval associated to one vertex has a nonempty
Results 1  10
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447,561