Add to ORKGA repetition is a sequence of symbols in which the first half is the\ud same as the second half. An edge-coloring of a graph is repetition-free if\ud there is no path with a color pattern that is a repetition. The minimum\ud number of colors so that a graph has an edge-coloring that is repetition-\ud free is called the Thue edge-chromatic number. In this thesis we investigate\ud the Thue edge-chromatic number of k-ary trees, that is trees in which every\ud vertex has at most k children. Specifically we obtain new upper and lower\ud bounds for the Thue edge-chromatic number of binary trees, and present a\ud new general method for obtaining repetition-free edge-colorings of k-ary trees\ud from what we call k-special sequences. We present exa...
An edge-coloring of a graph G with consecutive integers C1 ,..., Ct is called an interval t-coloring...
For positive integers m, n, the greatest number of colors that can appear in an edge coloring of K(m...
Trees are generalized to a special kind of higher dimensional complexes known as (j, k)-trees ([L.W....
A repetition is a sequence of symbols in which the first half is the same asthe second half. An edge...
A sequence S = s1s2:::s2n is called a repetition if si = sn+i for each i = 1;:::; n. A coloring of t...
A sequence is called non-repetitive if none of its subsequences forms a repetition (a sequence r1r2⋯...
International audienceA sequence r1, r2, ..., r2n such that ri=rn+ i for all 1≤i≤n is called a repet...
A harmonious colouring of a simple graph G is a proper vertex colouring such that each pair of colou...
For a fixed graph H, what is the smallest number of colours C such that there is a proper edge-colou...
Let us say a graph G has “tree-chromatic number” at most k if it admits a tree-decomposition (T, (X-...
Given a positive integer n and a family F of graphs, let R ∗ (n, F) denote the maximum number of col...
A sequence is called non-repetitive if none of its subsequences forms a repetition (a sequence r1r2...
AbstractA coloring of the vertices of a graph G is nonrepetitive if no path in G forms a sequence co...
The following seemingly simple question with surprisingly many connections to various problems in co...
AbstractThe set of problems we consider here are generalizations of square-free sequences [A. Thue, ...
An edge-coloring of a graph G with consecutive integers C1 ,..., Ct is called an interval t-coloring...
For positive integers m, n, the greatest number of colors that can appear in an edge coloring of K(m...
Trees are generalized to a special kind of higher dimensional complexes known as (j, k)-trees ([L.W....
A repetition is a sequence of symbols in which the first half is the same asthe second half. An edge...
A sequence S = s1s2:::s2n is called a repetition if si = sn+i for each i = 1;:::; n. A coloring of t...
A sequence is called non-repetitive if none of its subsequences forms a repetition (a sequence r1r2⋯...
International audienceA sequence r1, r2, ..., r2n such that ri=rn+ i for all 1≤i≤n is called a repet...
A harmonious colouring of a simple graph G is a proper vertex colouring such that each pair of colou...
For a fixed graph H, what is the smallest number of colours C such that there is a proper edge-colou...
Let us say a graph G has “tree-chromatic number” at most k if it admits a tree-decomposition (T, (X-...
Given a positive integer n and a family F of graphs, let R ∗ (n, F) denote the maximum number of col...
A sequence is called non-repetitive if none of its subsequences forms a repetition (a sequence r1r2...
AbstractA coloring of the vertices of a graph G is nonrepetitive if no path in G forms a sequence co...
The following seemingly simple question with surprisingly many connections to various problems in co...
AbstractThe set of problems we consider here are generalizations of square-free sequences [A. Thue, ...
An edge-coloring of a graph G with consecutive integers C1 ,..., Ct is called an interval t-coloring...
For positive integers m, n, the greatest number of colors that can appear in an edge coloring of K(m...
Trees are generalized to a special kind of higher dimensional complexes known as (j, k)-trees ([L.W....