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May 17, 2026Journal of Graph Theory0 citationsOpen Access

Lower Bounds for Maximum Weight Bisections of Weighted Triangle‐Free Subcubic Graphs

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SGStefanie GerkeRoyal Holloway University of LondonGGGregory GutinRoyal Holloway University of LondonAYAnders YeoUniversity of Southern Denmark

Key Points

  • The aim is to establish lower bounds for the weight of bisections in weighted triangle-free subcubic graphs.
  • Investigated properties of edge-weighted triangle-free subcubic graphs.
  • Conjectured that a particular lower bound can be improved.
  • Proved the conjecture for weighted bridgeless triangle-free cubic graphs.
  • Established that every weighted triangle-free subcubic graph has a bisection weight of at least a specific threshold.
  • Proved a conjectured improvement of this threshold for certain subclasses of graphs.

Abstract

ABSTRACT 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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Cite This Study

Gerke et al. (2026) studied this question.

synapsesocial.com/papers/6a095b1b7880e6d24efe0da9https://doi.org/10.1002/jgt.70056
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