Ascending Subgraph Decomposition
Kyriakos Katsamaktsis, Shoham Letzter, Alexey Pokrovskiy, Benny, Sudakov

TL;DR
This paper proves a conjecture from 1987 that large graphs with a specific number of edges can be decomposed into a sequence of subgraphs with increasing size, each isomorphic to a subgraph of the next.
Contribution
It confirms the conjecture for sufficiently large values of m, establishing a new result in graph decomposition theory.
Findings
Proves the conjecture for large m
Shows existence of ascending subgraph decompositions
Advances understanding of graph decomposition conditions
Abstract
A typical theme for many well-known decomposition problems is to show that some obvious necessary conditions for decomposing a graph into copies are also sufficient. One such problem was posed in 1987, by Alavi, Boals, Chartrand, Erd\H{o}s, and Oellerman. They conjectured that the edges of every graph with edges can be decomposed into subgraphs such that each has edges and is isomorphic to a subgraph of . In this paper we prove this conjecture for sufficiently large .
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Taxonomy
TopicsLimits and Structures in Graph Theory · graph theory and CDMA systems · Advanced Graph Theory Research
