Results 11 to 20 of about 6,056 (148)
Improper colouring of graphs with no odd clique minor [PDF]
Combinatorics, Probability and Computing, 2019 AbstractAs a strengthening of Hadwiger’s conjecture, Gerards and Seymour conjectured that every graph with no oddKtminor is (t− 1)-colourable. We prove two weaker variants of this conjecture. Firstly, we show that for eacht⩾ 2, every graph with no oddKtminor has a partition of its vertex set into 6t− 9 setsV1, …,V6t−9such that eachViinduces a subgraph ...
Sang-il Oum, Dong Yeap Kang
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Upward Three-Dimensional Grid Drawings of Graphs [PDF]
, 2005 A \emph{three-dimensional grid drawing} of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight line segments representing the edges do not cross. Our aim is to produce three-dimensional grid drawings
A. Garg +27 more
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The complexity of some acyclic improper colourings
Discrete Mathematics, 2011 AbstractIn this paper we will consider acyclic bipartition of the vertices of graphs, where acyclic means that the edges whose endpoints are in different parts of the partition induce a forest. We will require that the vertices belonging to the same partition induce graphs from particular class.
Katarzyna Jesse-Józefczyk +2 more
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IMPROPER COLORING OF WEIGHTED GRID AND HEXAGONAL GRAPHS [PDF]
Discrete Mathematics, Algorithms and Applications, 2010 We study a weighted improper coloring problem motivated by a frequency allocation problem. It consists of associating to each vertex a set of p(v) (weight) distinct colors (frequencies), such that the set of vertices having a given color induces a graph of degree at most k (the case k = 0 corresponds to proper coloring).
Bermond, Jean-Claude +3 more
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Edge intersection graphs of single bend paths on a grid [PDF]
Networks, 2005 AbstractWe combine the known notion of the edge intersection graphs of paths in a tree with a VLSI grid layout model to introduce the edge intersection graphs of paths on a grid. Let 𝒫 be a collection of nontrivial simple paths on a grid 𝒢. We define the edge intersection graph EPG(𝒫) of 𝒫 to have vertices which correspond to the members of 𝒫, such ...
Arie Tamir +3 more
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, 2004 A \emph{$(k,t)$-track layout} of a graph $G$ consists of a (proper) vertex $t$-colouring of $G$, a total order of each vertex colour class, and a (non-proper) edge $k$-colouring such that between each pair of colour classes no two monochromatic edges ...
Dujmovic, Vida +2 more
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Out-degree reducing partitions of digraphs [PDF]
, 2017 Let $k$ be a fixed integer. We determine the complexity of finding a $p$-partition $(V_1, \dots, V_p)$ of the vertex set of a given digraph such that the maximum out-degree of each of the digraphs induced by $V_i$, ($1\leq i\leq p$) is at least $k ...
Bang-Jensen, Joergen +3 more
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Obstructions to locally injective oriented improper colourings
European Journal of Combinatorics, 2014 Oriented colourings that are injective on in-neighbourhoods, but which need not be proper colourings, are considered. We first find some bounds on the number of colours needed, and determine the complexity of the associated decision problem. We then consider the polynomial cases, and describe efficient algorithms, based on colouring extensions, which ...
André Raspaud +2 more
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Modifying colourings between time-steps to tackle changes in dynamic random graphs [PDF]
, 2016 Many real world operational research problems can be formulated as graph colouring problems. Algorithms for this problem usually operate under the assumption that the size and constraints of a problem are fixed, allowing us to model the problem using a ...
Hardy, Bradley +2 more
core +1 more source
Tackling the edge dynamic graph colouring problem with and without future adjacency information [PDF]
, 2017 Many real world operational research problems, such as frequency assignment and exam timetabling, can be reformulated as graph colouring problems (GCPs). Most algorithms for the GCP operate under the assumption that its constraints are fixed, allowing us
Hardy, Bradley +2 more
core +2 more sources