Schultz, C.: Graph colourings, spaces of edges and spaces of circuits, Adv. Math. (to appear)Schu06] Carsten Schultz, Graph colorings, spaces of edges and spaces of circuits , Advances in Math. 221 (2006), no.
Matula, D.W., Marble, G., Isaacson, J.D.: Graph colouring algorithms. In: Read, R.C. (ed.) Graph Theory and Computing, pp. 109–122. Academic Press, New York (1972) Chapter Google Scholar Welsh, D.J.A., Powell, M.B.: An upper bound for chromatic number of a graph and ...
In the Maker–Breaker vertex colouring game, first publicised by Gardner in 1981, Maker and Breaker alternately colour vertices of a graph using a fixed palette, maintaining a proper colouring at all times. Maker aims to colour the whole graph, and Breaker aims to make some vertex impossible ...
Edge-colouringnon-propercolouringhereditarygraphpropertymaximumdegreeA graph property is any isomorphism-closed class of graphs. A property is hereditary if, whenever a graph G is in , and H is a subgraph of G, then H is also in . For a hereditary graph property ...
Graph Colouring Meets Deep Learning: Effective Graph Neural Network Models for Combinatorial Problems. arXiv 2019. paper. Diehl F, Brunner T, Le M T, et al. Graph Neural Networks for Modelling Traffic Participant Interaction. arXiv 2019. paper. Murphy R L, Srinivasan B, Rao V, et a...
CrossrefView in ScopusGoogle Scholar [23] Wu J. Graph marking game and colouring game (Ph.D. thesis) National Sun Yat-sen University (2005) Google Scholar [24] Wu J., Zhu X. Lower bounds for the game colouring number of planar graphs and partial k-trees Discrete Math., 308 (2008),...
Stated in [3]; Still Open There exists a function M:R→Z such that if mad(G)<4−2c+1−ϵ and Δ(G)>M(ϵ), then χℓ(G2)≤Δ(G)+c. Bonamy, Lévêque, and Pinlou’s result states that Conjecture 1.6 is true when c=1; we provide the strongest progress yet for whe...
(\exp \left(\frac{\pi }{8}[{\hat{S}}^{{\prime} },\hat{S}]\right)\). In the presence of bulk D3Vs, there is no consistent way of chequerboard colouring, hence the (arbitrarily chosen) grey regions. The top right shows that in a general stabilizer graph,\({\hat{S}}_{p}...
(nwmax))-time algorithm to compute an optimal bandwidth layout, wherenis the total number of vertices in the graph andwmaxis the maximum edge weight. For caterpillars with hair-length at mostk, we give ak-approximation algorithm. For arbitrary caterpillars and general graphs, we give a ...
We first examined the similarity landscape of the cell lines by performing a 2D projection of the raw and embedded GEx. By colouring the cell lines according to their tissue of origin, we visually verified the capacity of the CLL-gex-CLL embedding to resemble the raw GEx data (Fig.5a). ...