Matches in SemOpenAlex for { <https://semopenalex.org/work/W2951541835> ?p ?o ?g. }
Showing items 1 to 64 of
64
with 100 items per page.
- W2951541835 abstract "For graphs $G$ and $H$, an $H$-coloring of $G$ is an adjacency preserving map from the vertices of $G$ to the vertices of $H$. $H$-colorings generalize such notions as independent sets and proper colorings in graphs. There has been much recent research on the extremal question of finding the graph(s) among a fixed family that maximize or minimize the number of $H$-colorings. In this paper, we prove several results in this area. First, we find a class of graphs ${mathcal H}$ with the property that for each $H in {mathcal H}$, the $n$-vertex tree that minimizes the number of $H$-colorings is the path $P_n$. We then present a new proof of a theorem of Sidorenko, valid for large $n$, that for every $H$ the star $K_{1,n-1}$ is the $n$-vertex tree that maximizes the number of $H$-colorings. Our proof uses a stability technique which we also use to show that for any non-regular $H$ (and certain regular $H$) the complete bipartite graph $K_{2,n-2}$ maximizes the number of $H$-colorings of $n$-vertex $2$-connected graphs. Finally, we show that the cycle $C_n$ maximizes the number of proper colorings of $n$-vertex $2$-connected graphs." @default.
- W2951541835 created "2019-06-27" @default.
- W2951541835 creator A5041234298 @default.
- W2951541835 creator A5091067690 @default.
- W2951541835 date "2015-06-17" @default.
- W2951541835 modified "2023-09-27" @default.
- W2951541835 title "Extremal H-colorings of trees and 2-connected graphs" @default.
- W2951541835 cites W1593021638 @default.
- W2951541835 cites W1605313689 @default.
- W2951541835 cites W171464046 @default.
- W2951541835 cites W2056262613 @default.
- W2951541835 cites W2075240918 @default.
- W2951541835 cites W2077437403 @default.
- W2951541835 cites W2079035824 @default.
- W2951541835 cites W2155829240 @default.
- W2951541835 cites W2165469059 @default.
- W2951541835 cites W273178449 @default.
- W2951541835 cites W3022690009 @default.
- W2951541835 hasPublicationYear "2015" @default.
- W2951541835 type Work @default.
- W2951541835 sameAs 2951541835 @default.
- W2951541835 citedByCount "0" @default.
- W2951541835 crossrefType "posted-content" @default.
- W2951541835 hasAuthorship W2951541835A5041234298 @default.
- W2951541835 hasAuthorship W2951541835A5091067690 @default.
- W2951541835 hasConcept C114614502 @default.
- W2951541835 hasConcept C118615104 @default.
- W2951541835 hasConcept C132525143 @default.
- W2951541835 hasConcept C197657726 @default.
- W2951541835 hasConcept C33923547 @default.
- W2951541835 hasConcept C80899671 @default.
- W2951541835 hasConceptScore W2951541835C114614502 @default.
- W2951541835 hasConceptScore W2951541835C118615104 @default.
- W2951541835 hasConceptScore W2951541835C132525143 @default.
- W2951541835 hasConceptScore W2951541835C197657726 @default.
- W2951541835 hasConceptScore W2951541835C33923547 @default.
- W2951541835 hasConceptScore W2951541835C80899671 @default.
- W2951541835 hasLocation W29515418351 @default.
- W2951541835 hasOpenAccess W2951541835 @default.
- W2951541835 hasPrimaryLocation W29515418351 @default.
- W2951541835 hasRelatedWork W1964007319 @default.
- W2951541835 hasRelatedWork W2145702572 @default.
- W2951541835 hasRelatedWork W2276253431 @default.
- W2951541835 hasRelatedWork W2297336610 @default.
- W2951541835 hasRelatedWork W2539760540 @default.
- W2951541835 hasRelatedWork W2743273005 @default.
- W2951541835 hasRelatedWork W2773233663 @default.
- W2951541835 hasRelatedWork W2891169235 @default.
- W2951541835 hasRelatedWork W2949165654 @default.
- W2951541835 hasRelatedWork W2950671599 @default.
- W2951541835 hasRelatedWork W2962770462 @default.
- W2951541835 hasRelatedWork W2963861976 @default.
- W2951541835 hasRelatedWork W2979154907 @default.
- W2951541835 hasRelatedWork W2982287161 @default.
- W2951541835 hasRelatedWork W3100879432 @default.
- W2951541835 hasRelatedWork W3122637813 @default.
- W2951541835 hasRelatedWork W3128800975 @default.
- W2951541835 hasRelatedWork W3153778190 @default.
- W2951541835 hasRelatedWork W3163002073 @default.
- W2951541835 hasRelatedWork W3194359700 @default.
- W2951541835 isParatext "false" @default.
- W2951541835 isRetracted "false" @default.
- W2951541835 magId "2951541835" @default.
- W2951541835 workType "article" @default.