2 papers
math.CO2026
Every Minimal Counterexample to the ErdÅs-Gyárfás Conjecture is Predominantly Cubic
Avery Carr
A minimal counterexample to the ErdÅs-Gyárfás conjecture is a graph of minimum possible order and size with minimum degree at least 3 that contains no cycle whose length is a po…
math.CO2026
Cycles of Length 4 or 8 in Graphs with Diameter 2 and Minimum Degree at Least 3
Avery Carr
In this short note it is shown that every graph of diameter 2 and minimum degree at least 3 contains a cycle of length 4 or 8. This result contributes to the study of the ErdÅs-Gy…