Results 1  10
of
595
A dynamic survey of graph labellings
 Electron. J. Combin., Dynamic Surveys(6):95pp
, 2001
"... A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done ..."
Abstract

Cited by 167 (0 self)
 Add to MetaCart
A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been
Choosability of Graphs with Bounded Order: Ohba’s Conjecture and Beyond
, 2013
"... c©Jonathan A. Noel, 2013 The choice number of a graph G, denoted ch(G), is the minimum integer k such that for any assignment of lists of size k to the vertices of G, there is a proper colouring of G such that every vertex is mapped to a colour in its list. For general graphs, the choice number is ..."
Abstract
 Add to MetaCart
is not bounded above by a function of the chromatic number. In this thesis, we prove a conjecture of Ohba which asserts that ch(G) = χ(G) whenever V (G)  ≤ 2χ(G) + 1. We also prove a strengthening of Ohba’s Conjecture which is best possible for graphs on at most 3χ(G) vertices, and pose several conjectures
New Results in Graph Layout
 School of Computer Science, Carleton Univ
, 2003
"... A track layout of a graph consists of a vertex colouring, an edge colouring, and a total order of each vertex colour class such that between each pair of vertex colour classes, there is no monochromatic pair of crossing edges. This paper studies track layouts and their applications to other models o ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
of graph layout. In particular, we improve on the results of Enomoto and Miyauchi [SIAM J. Discrete Math., 1999] regarding stack layouts of subdivisions, and give analogous results for queue layouts. We solve open problems due to Felsner, Wismath, and Liotta [Proc. Graph Drawing, 2001] and Pach, Thiele
Embedding a Graph . . . Edgecrossings over the Spine
, 2005
"... A topological book embedding of a graph is an embedding in a book that carries the vertices in the spine of the book and the edges in the pages; edges are allowed to cross the spine. Enomoto showed that for any graph G having n vertices, there exists a threepage book embedding of G in which each e ..."
Abstract
 Add to MetaCart
A topological book embedding of a graph is an embedding in a book that carries the vertices in the spine of the book and the edges in the pages; edges are allowed to cross the spine. Enomoto showed that for any graph G having n vertices, there exists a threepage book embedding of G in which each
Repetition number of graphs
"... 1 Introduction A wellknown elementary exercise states that every graph (no loops or multiedges) has two vertices with the same degree. Motivated by this, we define the repetition number of a graph G, written rep(G), to be the maximum multiplicity in the list of vertex degrees. ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
1 Introduction A wellknown elementary exercise states that every graph (no loops or multiedges) has two vertices with the same degree. Motivated by this, we define the repetition number of a graph G, written rep(G), to be the maximum multiplicity in the list of vertex degrees.
Hadamard matrices, sequences, and block designs
 SONS, WILEYINTERSCIENCE SERIES IN DISCRETE MATHEMATICS AND OPTIMIZATION
, 1992
"... One hundred years ago, in 1893, Jacques Hadamard [31] found square matrices of orders 12 and 20, with entries ±1, which had all their rows (and columns) pairwise orthogonal. These matrices, X = (Xij), satisfied the equality of the following inequality, detX2 ≤ ∏ ∑ xij2, and so had maximal dete ..."
Abstract

Cited by 111 (36 self)
 Add to MetaCart
One hundred years ago, in 1893, Jacques Hadamard [31] found square matrices of orders 12 and 20, with entries ±1, which had all their rows (and columns) pairwise orthogonal. These matrices, X = (Xij), satisfied the equality of the following inequality, detX2 ≤ ∏ ∑ xij2, and so had maximal determinant among matrices with entries ±1. Hadamard actually asked the question of finding the maximal determinant of matrices with entries on the unit disc, but his name has become associated with the question concerning real matrices.
COUNTING LINKS IN COMPLETE GRAPHS
, 2006
"... Abstract. We find the minimal number of links in an embedding of any complete kpartite graph on 7 vertices (including K7, which has at least 21 links). We give either exact values or upper and lower bounds for the minimal number of links for all complete kpartite graphs on 8 vertices. We also look ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
look at larger complete bipartite graphs, and state a conjecture relating minimal linking embeddings with minimal book embeddings. 1.
Paths and Cycles in Graphs and Hypergraphs
, 1996
"... this paper. The general form is not needed, therefore only a special case is given here. In general the Acycle problem is to decide whether there exists a cycle containing all elements of A, where A is a collection of vertices and edges from the graph. But let us restrict ourselves to the case whe ..."
Abstract
 Add to MetaCart
this paper. The general form is not needed, therefore only a special case is given here. In general the Acycle problem is to decide whether there exists a cycle containing all elements of A, where A is a collection of vertices and edges from the graph. But let us restrict ourselves to the case
Results 1  10
of
595