
Finding Efficient Domination for P_8Free Bipartite Graphs in Polynomial Time
A vertex set D in a finite undirected graph G is an efficient dominating...
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Characterising ATfree Graphs with BFS
An asteroidal triple free graph is a graph such that for every independe...
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Graphical Construction of Spatial Gibbs Random Graphs
We present a Spatial Gibbs Random Graphs Model that incorporates the int...
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2× n Grids have Unbounded AnagramFree Chromatic Number
We show that anagramfree vertex colouring a 2× n square grid requires a...
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On the Leaders' Graphical Characterization for Controllability of Path Related Graphs
The problem of leaders location plays an important role in the controlla...
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Choosability with Separation of Cycles and Outerplanar Graphs
We consider the following list coloring with separation problem of graph...
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Colorcritical Graphs and Hereditary Hypergraphs
A quick proof of Gallai's celebrated theorem on colorcritical graphs is...
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Dichotomizing kvertexcritical Hfree graphs for H of order four
For k ≥ 3, we prove (i) there is a finite number of kvertexcritical (P_2+ℓ P_1)free graphs and (ii) kvertexcritical (P_3+P_1)free graphs have at most 2k1 vertices. Together with previous research, these results imply the following characterization where H is a graph of order four: There is a finite number of kvertexcritical Hfree graphs for fixed k ≥ 5 if and only if H is one of K_4, P_4, P_2 + 2P_1, or P_3 + P_1. Our results imply the existence of new polynomialtime certifying algorithms for deciding the kcolorability of (P_2+ℓ P_1)free graphs for fixed k.
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