NDLI: The Local Nature of List Colorings for Graphs of High Girth

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Vattani, Andrea Chierichetti, Flavio
Copyright Year	2010
Abstract	We consider list coloring problems for graphs $\mathcal{G}$ of girth larger than $c\log_{\Delta-1}n$, where n and $\Delta\geq3$ are, respectively, the order and the maximum degree of $\mathcal{G}$, and c is a suitable constant. First, we determine that the edge and total list chromatic numbers of these graphs are $\chi'_l(\mathcal{G})=\Delta$ and $\chi_l(\mathcal{G})=\Delta+1$. This proves that the general conjectures of Bollobs and Harris [Graphs Combin., 1 (1985), pp. 115127], Behzad [The total chromatic number, in Combinatorial Mathematics and Its Applications (Proc. Conf., Oxford, 1969), Academic Press, London, 1971, pp. 18], Vizing [Diskret. Analiz., 3 (1964), pp. 2530], and Juvan, Mohar, and krekovski [Combin. Probab. Comput., 7 (1998), pp. 181188] hold for this particular class of graphs. Moreover, our proofs exhibit a certain degree of locality, which we exploit to obtain an efficient distributed algorithm able to compute both kinds of optimal list colorings. Also, using an argument similar to one of Erds, we show that our algorithm can compute k-list vertex colorings of graphs having girth larger than $c\log_{k-1}n$.
Starting Page	2232
Ending Page	2250
Page Count	19
File Format	PDF
ISSN	00975397
DOI	10.1137/080732109
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	6 (Special Section On Foundations of Computer Science)
Volume Number	39
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-03-26
Access Restriction	Subscribed
Subject Keyword	algorithms girth graph coloring Graph algorithms Distributed algorithms Coloring of graphs and hypergraphs
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in