Matches in SemOpenAlex for { <https://semopenalex.org/work/W4298646085> ?p ?o ?g. }
Showing items 1 to 63 of
63
with 100 items per page.
- W4298646085 abstract "In this work we study the null space of bipartite graphs without cycles of length multiple of $4$, and its relation to structural properties. We decompose them into two subgraphs: $C_N(G)$ and $C_S(G)$. $C_N(G)$ has perfect matching and its adjacency matrix is nonsingular. $C_S(G)$ has a unique maximum independent set and the dimension of its null space equals the dimension of the null space of $G$. Even more, we show that the fundamental spaces of $G$ are the direct sum of the fundamental spaces of $C_N(G)$ and $C_S(G)$. We also obtain formulas relating the independence number and the matching number of a $C_{4k}$-free bipartite graph with $C_N(G)$ and $C_S(G)$, and the dimensions of the fundamental spaces. Among other results, we show that the rank of a $C_{4k}$-free bipartite graph is twice its matching number, generalizing a result for trees due to Bevis et al cite{bevis1995ranks}, and Cvetkovi'c and Gutman cite{D1972}. About maximum independent sets, we show that the intersection of all maximum independent sets of a $C_{4k}$-free bipartite graph coincides with the support of its null space." @default.
- W4298646085 created "2022-10-02" @default.
- W4298646085 creator A5007903041 @default.
- W4298646085 creator A5027039084 @default.
- W4298646085 creator A5046109777 @default.
- W4298646085 date "2018-10-13" @default.
- W4298646085 modified "2023-09-28" @default.
- W4298646085 title "On the null structure of bipartite graphs without cycles of length a multiple of 4" @default.
- W4298646085 doi "https://doi.org/10.48550/arxiv.1810.05802" @default.
- W4298646085 hasPublicationYear "2018" @default.
- W4298646085 type Work @default.
- W4298646085 citedByCount "0" @default.
- W4298646085 crossrefType "posted-content" @default.
- W4298646085 hasAuthorship W4298646085A5007903041 @default.
- W4298646085 hasAuthorship W4298646085A5027039084 @default.
- W4298646085 hasAuthorship W4298646085A5046109777 @default.
- W4298646085 hasBestOaLocation W42986460851 @default.
- W4298646085 hasConcept C105795698 @default.
- W4298646085 hasConcept C114614502 @default.
- W4298646085 hasConcept C118615104 @default.
- W4298646085 hasConcept C132525143 @default.
- W4298646085 hasConcept C138885662 @default.
- W4298646085 hasConcept C165064840 @default.
- W4298646085 hasConcept C180356752 @default.
- W4298646085 hasConcept C197657726 @default.
- W4298646085 hasConcept C203763787 @default.
- W4298646085 hasConcept C2778572836 @default.
- W4298646085 hasConcept C33676613 @default.
- W4298646085 hasConcept C33923547 @default.
- W4298646085 hasConcept C41008148 @default.
- W4298646085 hasConcept C41895202 @default.
- W4298646085 hasConcept C77088390 @default.
- W4298646085 hasConceptScore W4298646085C105795698 @default.
- W4298646085 hasConceptScore W4298646085C114614502 @default.
- W4298646085 hasConceptScore W4298646085C118615104 @default.
- W4298646085 hasConceptScore W4298646085C132525143 @default.
- W4298646085 hasConceptScore W4298646085C138885662 @default.
- W4298646085 hasConceptScore W4298646085C165064840 @default.
- W4298646085 hasConceptScore W4298646085C180356752 @default.
- W4298646085 hasConceptScore W4298646085C197657726 @default.
- W4298646085 hasConceptScore W4298646085C203763787 @default.
- W4298646085 hasConceptScore W4298646085C2778572836 @default.
- W4298646085 hasConceptScore W4298646085C33676613 @default.
- W4298646085 hasConceptScore W4298646085C33923547 @default.
- W4298646085 hasConceptScore W4298646085C41008148 @default.
- W4298646085 hasConceptScore W4298646085C41895202 @default.
- W4298646085 hasConceptScore W4298646085C77088390 @default.
- W4298646085 hasLocation W42986460851 @default.
- W4298646085 hasOpenAccess W4298646085 @default.
- W4298646085 hasPrimaryLocation W42986460851 @default.
- W4298646085 hasRelatedWork W2000352218 @default.
- W4298646085 hasRelatedWork W2143000384 @default.
- W4298646085 hasRelatedWork W2158949528 @default.
- W4298646085 hasRelatedWork W2349004882 @default.
- W4298646085 hasRelatedWork W2579720493 @default.
- W4298646085 hasRelatedWork W2798321768 @default.
- W4298646085 hasRelatedWork W2895884051 @default.
- W4298646085 hasRelatedWork W2950826653 @default.
- W4298646085 hasRelatedWork W3025390008 @default.
- W4298646085 hasRelatedWork W4298646085 @default.
- W4298646085 isParatext "false" @default.
- W4298646085 isRetracted "false" @default.
- W4298646085 workType "article" @default.