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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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Total perfect codes in graphs realized by commutative rings [PDF]
Transactions on Combinatorics, 2022 Let $R$ be a commutative ring with unity not equal to zero and let $\Gamma(R)$ be a zero-divisor graph realized by $R$. For a simple, undirected, connected graph $G = (V, E)$, a {\it total perfect code} denoted by $C(G)$ in $G$ is a subset $C(G ...
Rameez Raja
doaj +2 more sources
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
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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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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
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Perfect graphs for domination games [PDF]
Annals of Combinatorics, 2019 Let γ(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma (G)$$\end{
Csilla Bujtás +2 more
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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
core +3 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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Dual Perfect Bases and Dual Perfect Graphs [PDF]
, 2015 We introduce the notion of dual perfect bases and dual perfect graphs. We show that every integrable highest weight module $V_q(\lambda)$ over a quantum generalized Kac-Moody algebra $U_{q}(\mathcal{g})$ has a dual perfect basis and its dual perfect ...
Byeong Hoon Kahng +3 more
openalex +3 more sources