Erratum to the paper "Uniquely edge colourable graph"
Estimation of cut-vertices in edge-coloured complete graphs
Evaluating a weighted graph polynomial for graphs of bounded tree-width.
Existence and nonexistence of universal graphs
Exploiting the structure of conflict graphs in high level synthesis
In this paper we analyze the computational complexity of a processor optimization problem. Given operations with interval times in a branching flow graph, the problem is to find an assignment of the operations to a minimum number of processors. We analyze the complexity of this assignment problem for flow graphs with a constant number of program traces and a constant number of processors.
Extending Hall's theorem into list colorings: a partial history.
Extremal Crossing Numbers of Complete -Chromatic Graphs
Extremal problems for -partite and -colorable hypergraphs.
Extremal Properties of the Chromatic Polynomials of Connected 3-chromatic Graphs
Extreme distances in multicolored point sets.
Factorisation of snarks.
Fall coloring of graphs I
A fall coloring of a graph G is a proper coloring of the vertex set of G such that every vertex of G is a color dominating vertex in G (that is, it has at least one neighbor in each of the other color classes). The fall coloring number of G is the minimum size of a fall color partition of G (when it exists). Trivially, for any graph G, . In this paper, we show the existence of an infinite family of graphs G with prescribed values for χ(G) and . We also obtain the smallest non-fall colorable...
Fans and bundles in the graph of pairwise sums and products.
Few colored cuts or cycles in edge colored graphs
Flexible color lists in Alon and Tarsi's theorem, and time scheduling with unreliable participants.
Forbidden Structures for Planar Perfect Consecutively Colourable Graphs
A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose all induced...
Fractional Aspects of the Erdős-Faber-Lovász Conjecture
The Erdős-Faber-Lovász conjecture is the statement that every graph that is the union of n cliques of size n intersecting pairwise in at most one vertex has chromatic number n. Kahn and Seymour proved a fractional version of this conjecture, where the chromatic number is replaced by the fractional chromatic number. In this note we investigate similar fractional relaxations of the Erdős-Faber-Lovász conjecture, involving variations of the fractional chromatic number. We exhibit some relaxations that...
Fractional (P,Q)-Total List Colorings of Graphs
Let r, s ∈ N, r ≥ s, and P and Q be two additive and hereditary graph properties. A (P,Q)-total (r, s)-coloring of a graph G = (V,E) is a coloring of the vertices and edges of G by s-element subsets of Zr such that for each color i, 0 ≤ i ≤ r − 1, the vertices colored by subsets containing i induce a subgraph of G with property P, the edges colored by subsets containing i induce a subgraph of G with property Q, and color sets of incident vertices and edges are disjoint. The fractional (P,Q)-total...
Fractional Q-Edge-Coloring of Graphs
An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let [...] be an additive hereditary property of graphs. A [...] -edge-coloring of a simple graph is an edge coloring in which the edges colored with the same color induce a subgraph of property [...] . In this paper we present some results on fractional [...] -edge-colorings. We determine the fractional [...] -edge chromatic number for matroidal properties of graphs.
Frequency planning and ramifications of coloring
This paper surveys frequency assignment problems coming up in planning wireless communication services. It particularly focuses on cellular mobile phone systems such as GSM, a technology that revolutionizes communication. Traditional vertex coloring provides a conceptual framework for the mathematical modeling of many frequency planning problems. This basic form, however, needs various extensions to cover technical and organizational side constraints. Among these ramifications are T-coloring and...