![]() ![]() ![]() Journal of the Australian Mathematical Society, 105(1):79-102, 2018.Įxtension from precoloured sets of edges ( PDF - Journal - BibTeX) The Electronic Journal of Combinatorics, 26(1):#P1.51, 14pp., 2019.Įxpander graphs and sieving in combinatorial structures ( PDF - Journal - BibTeX) On generalized choice and coloring numbers ( PDF - Journal - BibTeX) Mixed Circular Codes ( PDF - Journal - BibTeX) Isomorphism of Weighted Trees and Stanley's Isomorphism Conjecture for Caterpillars ( PDF - Journal - BibTeX)Īnnales de l’Institut Henri Poincaré D 6(3):357-384, 2019. The Electronic Journal of Combinatorics 27(1):#P1.8, 14 pp., 2020.Ī 4-choosable graph that is not (8:2)-choosable ( PDF - Journal - BibTeX) Variations on the Petersen colouring conjecture ( PDF - Journal - BibTeX) Revisiting a theorem by Folkman on graph colouring ( PDF - Journal - BibTeX) The relation between k-circularity and circularity of codes ( PDF - Journal - BibTeX)īulletin of Mathematical Biology 82:105, 2020.Įccentricity of Networks with Structural Constraints ( PDF - Journal - BibTeX)ĭiscussiones Mathematicae Graph Theory 40:1141-1162, 2020. On fractional fragility rates of graph classes ( PDF - Journal - BibTeX) SIAM Journal on Discrete Mathematics 35(2):1136-1148, 2021.įractional chromatic number, maximum degree and girth ( PDF - Journal - BibTeX) Trinucleotide k-circular codes I: Theory ( PDF - Journal - BibTeX)īipartite independence number in graphs with bounded maximum degree ( PDF - Journal - BibTeX) Trinucleotide k-circular codes II: Biology ( PDF - Journal - BibTeX) Mathematics of Operations Research, à paraître. We further apply these algorithms to get efficient algorithms for a geometric problem namely the Terrain Guarding problem, when parameterised by a structural parameter.On the effect of symmetry requirement for rendezvous on the complete graph ( PDF - Archive ouverte - BibTeX) We show that this problem is in FPT when parameterised by both the treewidth and the solution size. This result stands in contrast to general graphs where the CF-chromatic number can be $$\varOmega (\sqrt of $G$ refers to coloring a subset of $V$ such that every vertex $v$ has at least one colored vertex in its closed neighborhood and moreover all the colored vertices in $v$'s neighborhood have distinct colors. On the CF-chromatic number of any string graph G with n vertices in terms of the classical chromatic number $$\chi (G)$$ In this paper we obtain such bounds for several classes of string graphs, i.e., intersection graphs of curves in the plane: (i) we provide a general upper bound of $$O(\chi (G)^2 \log n)$$ Bounds on CF-chromatic numbers have been studied both for general graphs and for intersection graphs of geometric shapes. Is a coloring of V such that the punctured neighborhood of each vertex contains a vertex whose color differs from the color of any other vertex in that neighborhood. We also study the closed neighborhood variant of the problem denoted by CFCN*, and obtain analogous results in some of the above cases.read more read lessĪbstract: Conflict-free coloring (in short, CF-coloring) of a graph $$G = (V,E)$$ For Kneser graphs $K(n,k)$, when $n\geq k(k 1)^2 1$, we show that the CFON* chromatic number is $k 1$. For split graphs, we show that the problem is NP-complete. We also study the problem on split graphs and Kneser graphs. Moreover, we give upper bounds for the CFON* chromatic number on unit square and unit disk graphs. We give tight bounds of two and three for the CFON* chromatic number for proper interval graphs and interval graphs. We study the problem on the following intersection graphs: interval graphs, unit square graphs and unit disk graphs. For both graph classes, we give tight bounds of three and two respectively for the CFON* chromatic number. We study the problem on block graphs and cographs, which have bounded clique width. ![]() The CFON* problem is fixed-parameter tractable with respect to the combined parameters clique width and the solution size. In this paper, we show the following results. The decision version of the CFON* problem is NP-complete even on planar graphs. The minimum number of colors required for such a coloring is called the conflict-free chromatic number. Abstract: Given an undirected graph, a conflict-free coloring (CFON*) is an assignment of colors to a subset of the vertices of the graph such that for every vertex there exists a color that is assigned to exactly one vertex in its open neighborhood. ![]()
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