Matches in SemOpenAlex for { <https://semopenalex.org/work/W4380551471> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W4380551471 abstract "In the inhomogeneous random graph model, each vertex $iin{1,ldots,n}$ is assigned a weight $W_isimtext{Unif}(0,1)$, and an edge between any two vertices $i,j$ is present with probability $k(W_i,W_j)/lambda_nin[0,1]$, where $k$ is a positive, symmetric function and $lambda_n$ is a scaling parameter that controls the graph density. When $lambda_n=1$ (resp.~$lambda_n=O(n)$) the typical resulting graph is dense (resp.~sparse). The goal of this paper is the study of structural properties of textit{large} inhomogeneous random graphs. We focus our attention on graph functions that grow sufficiently slowly as the graph size increases. Under some additional technical assumptions, we show that the first-order asymptotic behavior of all such properties is the same for the inhomogeneous random graph and for the ErdH{o}s-R'enyi random graph. Our proof relies on two couplings between the inhomogeneous random graph and appropriately constructed ErdH{o}s-R'enyi random graphs. We demonstrate our method by obtaining asymptotics for two structural properties of the inhomogeneous random graph which were previously unknown. In the sparse regime, we find the leading-order term for the chromatic number. In the dense regime, we find the asymptotics of the so-called $gamma$-quasi-clique number." @default.
- W4380551471 created "2023-06-14" @default.
- W4380551471 creator A5008502624 @default.
- W4380551471 creator A5022935854 @default.
- W4380551471 creator A5036879000 @default.
- W4380551471 date "2023-06-10" @default.
- W4380551471 modified "2023-09-26" @default.
- W4380551471 title "First-order asymptotics for the structure of the inhomogeneous random graph" @default.
- W4380551471 doi "https://doi.org/10.48550/arxiv.2306.06396" @default.
- W4380551471 hasPublicationYear "2023" @default.
- W4380551471 type Work @default.
- W4380551471 citedByCount "0" @default.
- W4380551471 crossrefType "posted-content" @default.
- W4380551471 hasAuthorship W4380551471A5008502624 @default.
- W4380551471 hasAuthorship W4380551471A5022935854 @default.
- W4380551471 hasAuthorship W4380551471A5036879000 @default.
- W4380551471 hasBestOaLocation W43805514711 @default.
- W4380551471 hasConcept C114614502 @default.
- W4380551471 hasConcept C118615104 @default.
- W4380551471 hasConcept C121332964 @default.
- W4380551471 hasConcept C132525143 @default.
- W4380551471 hasConcept C203776342 @default.
- W4380551471 hasConcept C2524010 @default.
- W4380551471 hasConcept C2778113609 @default.
- W4380551471 hasConcept C33923547 @default.
- W4380551471 hasConcept C4255713 @default.
- W4380551471 hasConcept C43517604 @default.
- W4380551471 hasConcept C47458327 @default.
- W4380551471 hasConcept C62520636 @default.
- W4380551471 hasConcept C80899671 @default.
- W4380551471 hasConcept C99844830 @default.
- W4380551471 hasConceptScore W4380551471C114614502 @default.
- W4380551471 hasConceptScore W4380551471C118615104 @default.
- W4380551471 hasConceptScore W4380551471C121332964 @default.
- W4380551471 hasConceptScore W4380551471C132525143 @default.
- W4380551471 hasConceptScore W4380551471C203776342 @default.
- W4380551471 hasConceptScore W4380551471C2524010 @default.
- W4380551471 hasConceptScore W4380551471C2778113609 @default.
- W4380551471 hasConceptScore W4380551471C33923547 @default.
- W4380551471 hasConceptScore W4380551471C4255713 @default.
- W4380551471 hasConceptScore W4380551471C43517604 @default.
- W4380551471 hasConceptScore W4380551471C47458327 @default.
- W4380551471 hasConceptScore W4380551471C62520636 @default.
- W4380551471 hasConceptScore W4380551471C80899671 @default.
- W4380551471 hasConceptScore W4380551471C99844830 @default.
- W4380551471 hasLocation W43805514711 @default.
- W4380551471 hasOpenAccess W4380551471 @default.
- W4380551471 hasPrimaryLocation W43805514711 @default.
- W4380551471 hasRelatedWork W1746482425 @default.
- W4380551471 hasRelatedWork W1983682594 @default.
- W4380551471 hasRelatedWork W1994148577 @default.
- W4380551471 hasRelatedWork W2167810763 @default.
- W4380551471 hasRelatedWork W2171385678 @default.
- W4380551471 hasRelatedWork W2949510659 @default.
- W4380551471 hasRelatedWork W2952539738 @default.
- W4380551471 hasRelatedWork W3195351302 @default.
- W4380551471 hasRelatedWork W4292734940 @default.
- W4380551471 hasRelatedWork W4300413005 @default.
- W4380551471 isParatext "false" @default.
- W4380551471 isRetracted "false" @default.
- W4380551471 workType "article" @default.