Results 1 to 10 of about 1,679,013 (321)
Defective Coloring on Classes of Perfect Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 In Defective Coloring we are given a graph $G$ and two integers $\chi_d$, $\Delta^*$ and are asked if we can $\chi_d$-color $G$ so that the maximum degree induced by any color class is at most $\Delta^*$.
Rémy Belmonte +2 more
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Characterising and recognising game-perfect graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 Consider a vertex colouring game played on a simple graph with $k$ permissible colours. Two players, a maker and a breaker, take turns to colour an uncoloured vertex such that adjacent vertices receive different colours.
Dominique Andres, Edwin Lock
doaj +3 more sources
Partitioning Perfect Graphs into Stars [PDF]
Journal of Graph Theory, 2016 The partition of graphs into "nice" subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into same-size stars, a problem known to be NP-complete even for the case of stars on three
Bredereck, Robert +6 more
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Parameterized Algorithms on Perfect Graphs for deletion to $(r,\ell)$-graphs [PDF]
International Symposium on Mathematical Foundations of Computer Science, 2015 For fixed integers $r,\ell \geq 0$, a graph $G$ is called an {\em $(r,\ell)$-graph} if the vertex set $V(G)$ can be partitioned into $r$ independent sets and $\ell$ cliques. The class of $(r, \ell)$ graphs generalizes $r$-colourable graphs (when $\ell =0)
Kolay, Sudeshna +3 more
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Perfect graphs of arbitrarily large clique-chromatic number [PDF]
J. Comb. Theory B, 2015 We prove that there exist perfect graphs of arbitrarily large clique-chromatic number. These graphs can be obtained from cobipartite graphs by repeatedly gluing along cliques. This negatively answers a question raised by Duffus, Sands, Sauer, and Woodrow
Charbit, Pierre +3 more
core +4 more sources
Random Struct. Algorithms, 2017 We investigate the asymptotic structure of a random perfect graph $P_n$ sampled uniformly from the perfect graphs on vertex set $\{1,\ldots,n\}$. Our approach is based on the result of Pr\"omel and Steger that almost all perfect graphs are generalised ...
McDiarmid, Colin, Yolov, Nikola
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A new characterization of trivially perfect graphs
Electronic Journal of Graph Theory and Applications, 2015 A graph $G$ is \emph{trivially perfect} if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number) $\alpha(G)$ equals the number of (maximal) cliques $m(G)$.
Christian Rubio Montiel
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Perfect state transfer, graph products and equitable partitions [PDF]
, 2010 We describe new constructions of graphs which exhibit perfect state transfer on continuous-time quantum walks. Our constructions are based on variants of the double cones [BCMS09,ANOPRT10,ANOPRT09] and the Cartesian graph products (which includes the n ...
Ge, Yang +3 more
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Submodular Functions and Perfect Graphs [PDF]
Mathematics of Operations Research, 2021 We give a combinatorial polynomial-time algorithm to find a maximum weight independent set in perfect graphs of bounded degree that do not contain a prism or a hole of length four as an induced subgraph.
Tara Abrishami +3 more
semanticscholar +1 more source
The spanning k-trees, perfect matchings and spectral radius of graphs [PDF]
Linear and multilinear algebra, 2021 A k-tree is a spanning tree in which every vertex has degree at most k. In this paper, we provide a sufficient condition for the existence of a k-tree in a connected graph with fixed order in terms of the adjacency spectral radius and the signless ...
Dandan Fan +3 more
semanticscholar +1 more source