
On graphs with no induced fivevertex path or paraglider
Given two graphs H_1 and H_2, a graph is (H_1, H_2)free if it contains ...
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An Optimal χBound for (P_6, diamond)Free Graphs
Given two graphs H_1 and H_2, a graph G is (H_1,H_2)free if it contains...
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Coloring graphs with no induced fivevertex path or gem
For a graph G, let χ(G) and ω(G) respectively denote the chromatic numbe...
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Squarefree graphs with no sixvertex induced path
We elucidate the structure of (P_6,C_4)free graphs by showing that ever...
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Colouring SquareFree Graphs without Long Induced Paths
The complexity of Colouring is fully understood for Hfree graphs, but ...
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Structural domination and coloring of some (P_7, C_7)free graphs
We show that every connected induced subgraph of a graph G is dominated ...
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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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Wheelfree graphs with no induced fivevertex path
A 4wheel is the graph consisting of a chordless cycle on four vertices C_4 plus an additional vertex adjacent to all the vertices of the C_4. In this paper, we explore the structure of (P_5,4wheel)free graphs, and show that every such graph G is either perfect, or a quasiline graph, or has a clique cutset, or G belongs to some welldefined special classes of graphs. This result enables us to show that every (P_5,4wheel)free graph G satisfies χ(G)≤3/2ω(G). Moreover, this bound is asymptotically tight. That is, there is a class of (P_5,4wheel)free graphs H such that every graph H∈ H satisfies χ(H)≥10/7ω(H).
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