ﻻ يوجد ملخص باللغة العربية
A graph is locally irregular if any pair of adjacent vertices have distinct degrees. A locally irregular decomposition of a graph $G$ is a decomposition $mathcal{D}$ of $G$ such that every subgraph $H in mathcal{D}$ is locally irregular. A graph is said to be decomposable if it admits a locally irregular decomposition. We prove that any decomposable split graph can be decomposed into at most three locally irregular subgraphs and we characterize all split graphs whose decomposition can be into one, two or three locally irregular subgraphs.
Given a graph $G$, a decomposition of $G$ is a partition of its edges. A graph is $(d, h)$-decomposable if its edge set can be partitioned into a $d$-degenerate graph and a graph with maximum degree at most $h$. For $d le 4$, we are interested in the
We prove that for $k in mathbb{N}$ and $d leq 2k+2$, if a graph has maximum average degree at most $2k + frac{2d}{d+k+1}$, then $G$ decomposes into $k+1$ pseudoforests, where one of the pseudoforests has all connected components having at most $d$ edges.
For a real constant $alpha$, let $pi_3^alpha(G)$ be the minimum of twice the number of $K_2$s plus $alpha$ times the number of $K_3$s over all edge decompositions of $G$ into copies of $K_2$ and $K_3$, where $K_r$ denotes the complete graph on $r$ ve
In 2006, Barat and Thomassen posed the following conjecture: for each tree $T$, there exists a natural number $k_T$ such that, if $G$ is a $k_T$-edge-connected graph and $|E(G)|$ is divisible by $|E(T)|$, then $G$ admits a decomposition into copies o
A graph $G$ is called interval colorable if it has a proper edge coloring with colors $1,2,3,dots$ such that the colors of the edges incident to every vertex of $G$ form an interval of integers. Not all graphs are interval colorable; in fact, quite f