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complete graph
"... Let F be a (not necessarily commutative) field and m,n ≥ 1. Gn+m,m(F) denotes the Grassmannian of all msubspaces of the left vector space F n+m. Two msubspaces W1 and W2 are called adjacent if dimW1 ∩W2 = m−1. We consider Gn+m,m(F) as the set of vertices of an undirected graph, called the Grassman ..."
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Let F be a (not necessarily commutative) field and m,n ≥ 1. Gn+m,m(F) denotes the Grassmannian of all msubspaces of the left vector space F n+m. Two msubspaces W1 and W2 are called adjacent if dimW1 ∩W2 = m−1. We consider Gn+m,m(F) as the set of vertices of an undirected graph, called
SUBGRAPHS OF COMPLETE GRAPH
"... Abstract: In the complete graph K2m+3 for m ≥ 2, we study some structures of simple nonisomorphic Hamiltonian subgraphs of the form H ( 2m+3, 6m+3) for m ≥ 2. The various structures of the form H(2m+3, 6m+3) for m ≥ 2 are found and some of them are observed to give some forms of metal atom cluster ..."
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Cited by 1 (1 self)
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Abstract: In the complete graph K2m+3 for m ≥ 2, we study some structures of simple nonisomorphic Hamiltonian subgraphs of the form H ( 2m+3, 6m+3) for m ≥ 2. The various structures of the form H(2m+3, 6m+3) for m ≥ 2 are found and some of them are observed to give some forms of metal atom
ENUMERATION OF WEIGHTED COMPLETE GRAPHS
"... Abstract. We enumerate the number of weighted complete graphs and compute its generating function. 1. ..."
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Abstract. We enumerate the number of weighted complete graphs and compute its generating function. 1.
Geometric Thickness of Complete Graphs
 J. GRAPH ALGORITHMS APPL
, 2000
"... We define the geometric thickness of a graph to be the smallest number of layers such that we can draw the graph in the plane with straightline edges and assign each edge to a layer so that no two edges on the same layer cross. The geometric thickness lies between two previously studied quantiti ..."
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Cited by 33 (4 self)
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quantities, the (graphtheoretical) thickness and the book thickness. We investigate the geometric thickness of the family of complete graphs, {Kn}. We show that the geometric thickness of Kn lies between #(n/5.646) + 0.342# and #n/4#, and we give exact values of the geometric thickness of Kn for n
COMPLETE GRAPHS AND SMALL GRAPHS WITH STRICT
, 2013
"... The combinatorial inverse eigenvalue problems: complete graphs and small graphs with strict inequality ..."
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The combinatorial inverse eigenvalue problems: complete graphs and small graphs with strict inequality
On CliqueComplete Graphs
 Discrete Math
, 1992
"... A graph is cliquecomplete if no two of its maximal cliques are disjoint. A vertex is universal if it is adjacent to all other vertices in the graph. We prove that every cliquecomplete graph either contains a universal vertex or an induced subgraph in an indexed family Q := fQ 2n+1 : n 1g, defined ..."
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A graph is cliquecomplete if no two of its maximal cliques are disjoint. A vertex is universal if it is adjacent to all other vertices in the graph. We prove that every cliquecomplete graph either contains a universal vertex or an induced subgraph in an indexed family Q := fQ 2n+1 : n 1g
Layered percolation on the complete graph
, 2009
"... ABSTRACT. We present a generalized (multitype) version of percolation on the complete graph, in which we divide the vertices of the graph into a fixed number of sets (called layers) and perform percolation where the probability of {u, v} being in our edge set depends on the respective layers of u an ..."
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Cited by 2 (0 self)
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ABSTRACT. We present a generalized (multitype) version of percolation on the complete graph, in which we divide the vertices of the graph into a fixed number of sets (called layers) and perform percolation where the probability of {u, v} being in our edge set depends on the respective layers of u
ON SWELL–COLORED COMPLETE GRAPHS
, 1994
"... Abstract. An edgecolored graph is said to be swellcolored if each triangle contains exactly 1 or 3 colors but never 2 colors and if the graph contains more than one color. It is shown that a swellcolored complete graph with n vertices contains at least √ n + 1 colors. The complete graph with n2 v ..."
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Cited by 1 (0 self)
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Abstract. An edgecolored graph is said to be swellcolored if each triangle contains exactly 1 or 3 colors but never 2 colors and if the graph contains more than one color. It is shown that a swellcolored complete graph with n vertices contains at least √ n + 1 colors. The complete graph with n2
Partial profiles of quasicomplete graphs
, 2008
"... We enumerate graph homomorphisms to quasicomplete graphs i.e., graphs obtained from complete graphs by removing one edge. The source graphs are complete graphs, quasicomplete graphs, cycles, paths, wheels and broken wheels. ..."
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We enumerate graph homomorphisms to quasicomplete graphs i.e., graphs obtained from complete graphs by removing one edge. The source graphs are complete graphs, quasicomplete graphs, cycles, paths, wheels and broken wheels.
Packings in Complete Graphs
"... We deal with the concept of packings in graphs, which may be regarded as a generalization of the theory of graph design. In particular we construct a vertex and edgedisjoint packing of Kn (where n/2 mod 4 equals 0 or 1) with edges of different cyclic length. Moreover we consider edgedisjoint pac ..."
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disjoint packings in complete graphs with uniform linear forests (and the resulting packings have special additional properties). Further we give a relationship between finite geometries and certain packings which suggests interesting questions.
Results 1  10
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1,050,158