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Demonstrates lower bounds for maximum weight bisections in triangle-free subcubic graphs, suggesting important implications for graph theory.
A bisection of a graph is a cut in which the number of vertices in the two parts of the cut differ by at most 1. In this paper, we consider maximum weight bisections of edge‐weighted triangle‐free subcubic graphs and show that every weighted triangle‐free subcubic graph has a bisection with weight at least unless (where ). We conjecture that can be replaced by , the value of for the Peterson graph and prove the conjecture for weighted bridgeless triangle‐free cubic graphs.
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Gerke et al. (2026) studied this question.
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