On decomposing multigraphs into locally irregular submultigraphs
نویسندگان
چکیده
A locally irregular multigraph is a whose adjacent vertices have distinct degrees. The edge coloring an of G such that every color induces submultigraph G. We say colorable if it admits and we denote by lir(G) the chromatic index G, which smallest number colors required in conjecture for connected graph not isomorphic to K2, 2G obtained from doubling each lir(2G)≤2. This concept closely related well known 1-2-3 Conjecture, Local Irregularity (2, 2) Conjecture other similar problems concerning colorings. show this holds classes like paths, cycles, wheels, complete graphs, k-partite graphs bipartite graphs. also prove general bound all 2-multigraphs using our result
منابع مشابه
Decomposing oriented graphs into 6 locally irregular oriented graphs
An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪ ...∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently conjectured by Baudon et al. that every undirected graph admits a decomposition into 3 locally irre...
متن کاملDecomposing Oriented Graphs into Six Locally Irregular Oriented Graphs
An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪ ...∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently conjectured by Baudon et al. that every undirected graph admits a decomposition into 3 locally irre...
متن کاملOn Decomposing Graphs of Large Minimum Degree into Locally Irregular Subgraphs
A locally irregular graph is a graph whose adjacent vertices have distinct degrees. We say that a graph G can be decomposed into k locally irregular subgraphs if its edge set may be partitioned into k subsets each of which induces a locally irregular subgraph in G. It has been conjectured that apart from the family of exceptions which admit no such decompositions, i.e., odd paths, odd cycles an...
متن کاملCounting irregular multigraphs
Gagliardi et al. (1996, unpublished manuscript) defined an irregular multigraph to be a loopless multigraph with degree sequence n, n 1 . . . . . 1, and they posed the problem of determining the number of different irregular multigraphs f , on n vertices. In Gagliardi et al. (1996) they showed that if n 0 or 3 (mod 4) then f , > n 1. In this note our aim is to show that there are constants 1 < ...
متن کاملDecomposing Semi-complete Multigraphs and Directed Graphs into Paths of Length Two
A P3-decomposition of a graph is a partition of the edges of the graph into paths of length two. We give a necessary and sufficient condition for a semi-complete multigraph, that is a multigraph with at least one edge between each pair of vertices, to have a P3-decomposition. We show that this condition can be tested in strongly polynomial-time, and that the same condition applies to a larger c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2023
ISSN: ['1873-5649', '0096-3003']
DOI: https://doi.org/10.1016/j.amc.2023.128049