A Ramsey Goodness Result for Graphs with Many Pendant Edges

Burr has shown that if \(G\) is any graph without isolates and \(H_0\) is any connected graph, every graph \(H\) obtained from \(H_0\) by subdividing a chosen edge sufficiently many times to create a long suspended path satisfies \(r(G, H) = (x(G) – 1)(|V(H)| – 1) + s(G)\), where \(s(G)\) is the largest number such that in every proper coloring of \(V(G)\) using \(\chi(G)\) colors, every color class has at least \(s(G)\) elements. In this paper, we prove a companion result for graphs obtained from \(H_0\) by adding sufficiently many pendant edges.