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Creators/Authors contains: "Karthick, T."

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  1. ; ; ; (, The Electronic Journal of Combinatorics)
    null (Ed.)
    The claw is the graph $$K_{1,3}$$, and the fork is the graph obtained from the claw $$K_{1,3}$$ by subdividing one of its edges once. In this paper, we prove a structure theorem for the class of (claw, $$C_4$$)-free graphs that are not quasi-line graphs, and a structure theorem for the class of (fork, $$C_4$$)-free graphs that uses the class of (claw, $$C_4$$)-free graphs as a basic class. Finally, we show that every (fork, $$C_4$$)-free graph $$G$$ satisfies $$\chi(G)\leqslant \lceil\frac{3\omega(G)}{2}\rceil$$ via these structure theorems with some additional work on coloring basic classes. 
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  2. ; ; ; (, Journal of Graph Theory)
    For a graph 𝐺 , let 𝜒(𝐺) and 𝜔(𝐺) , respectively, denote the chromatic number and clique number of 𝐺 . We give an explicit structural description of ( 𝑃5 , gem)‐free graphs, and show that every such graph 𝐺 satisfies 𝜒(𝐺)≤⌈5𝜔(𝐺)4⌉ . Moreover, this bound is best possible. Here a gem is the graph that consists of an induced four‐vertex path plus a vertex which is adjacent to all the vertices of that path. 
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