Optimal Acyclic Edge Colouring of Grid Like Graphs

2006 ◽  
pp. 360-367 ◽  
Author(s):  
Rahul Muthu ◽  
N. Narayanan ◽  
C. R. Subramanian
Keyword(s):  
Edge Colouring

scholarly journals Bounds and complexity results for strong edge colouring of subcubic graphs

2011 ◽  
Vol 38 ◽  
pp. 463-468
Author(s):  
Hervé Hocquard ◽  
Pascal Ochem ◽  
Petru Valicov
Keyword(s):  
Complexity Results ◽  
Subcubic Graphs ◽  
Edge Colouring

scholarly journals Edge colouring line graphs of unicyclic graphs

1992 ◽  
Vol 36 (1) ◽  
pp. 75-82 ◽  
Author(s):  
Leizhen Cai ◽  
John A. Ellis
Keyword(s):  
Line Graphs ◽  
Unicyclic Graphs ◽  
Edge Colouring

scholarly journals Characterizing and edge-colouring split-indifference graphs

1998 ◽  
Vol 82 (1-3) ◽  
pp. 209-217 ◽  
Author(s):  
Z. Carmen Ortiz ◽  
Nelson Maculan ◽  
Jayme L. Szwarcfiter
Keyword(s):  
Edge Colouring

Edge Colouring Reduced Indifference Graphs

2000 ◽  
pp. 145-153
Author(s):  
Celina M. H. de Figueiredo ◽  
Célia Picinin de Mello ◽  
Carmen Ortiz
Keyword(s):  
Edge Colouring

Edge-colouring graphs with bounded local degree sums

2020 ◽  
Vol 281 ◽  
pp. 268-283
Author(s):  
L.M. Zatesko ◽  
A. Zorzi ◽  
R. Carmo ◽  
A.L.P. Guedes
Keyword(s):  
Local Degree ◽  
Edge Colouring

scholarly journals Constrained Ramsey Numbers

2009 ◽  
Vol 18 (1-2) ◽  
pp. 247-258 ◽  
Author(s):  
PO-SHEN LOH ◽  
BENNY SUDAKOV
Keyword(s):  
Complete Graph ◽  
Ramsey Number ◽  
Ramsey Numbers ◽  
Ramsey Theorem ◽  
Logarithmic Factor ◽  
Subgraph Isomorphic ◽  
Rate Of Growth ◽  
Special Cases ◽  
Edge Colouring

For two graphs S and T, the constrained Ramsey number f(S, T) is the minimum n such that every edge colouring of the complete graph on n vertices (with any number of colours) has a monochromatic subgraph isomorphic to S or a rainbow subgraph isomorphic to T. Here, a subgraph is said to be rainbow if all of its edges have different colours. It is an immediate consequence of the Erdős–Rado Canonical Ramsey Theorem that f(S, T) exists if and only if S is a star or T is acyclic. Much work has been done to determine the rate of growth of f(S, T) for various types of parameters. When S and T are both trees having s and t edges respectively, Jamison, Jiang and Ling showed that f(S, T) ≤ O(st2) and conjectured that it is always at most O(st). They also mentioned that one of the most interesting open special cases is when T is a path. In this paper, we study this case and show that f(S, Pt) = O(st log t), which differs only by a logarithmic factor from the conjecture. This substantially improves the previous bounds for most values of s and t.

scholarly journals Star multigraphs with three vertices of maximum degree

1986 ◽  
Vol 100 (2) ◽  
pp. 303-317 ◽  
Author(s):  
A. G. Chetwynd ◽  
A. J. W. Hilton
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Special Kind ◽  
Chromatic Index ◽  
Simple Graphs ◽  
Multiple Edges ◽  
Image Position ◽  
Edge Colouring

The graphs we consider here are either simple graphs, that is they have no loops or multiple edges, or are multigraphs, that is they may have more than one edge joining a pair of vertices, but again have no loops. In particular we shall consider a special kind of multigraph, called a star-multigraph: this is a multigraph which contains a vertex v*, called the star-centre, which is incident with each non-simple edge. An edge-colouring of a multigraph G is a map ø: E(G)→, where is a set of colours and E(G) is the set of edges of G, such that no two edges receiving the same colour have a vertex in common. The chromatic index, or edge-chromatic numberχ′(G) of G is the least value of || for which an edge-colouring of G exists. Generalizing a well-known theorem of Vizing [14], we showed in [6] that, for a star-multigraph G,where Δ(G) denotes the maximum degree (that is, the maximum number of edges incident with a vertex) of G. Star-multigraphs for which χ′(G) = Δ(G) are said to be Class 1, and otherwise they are Class 2.

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