7,546 research outputs found
Graph homomorphisms, the Tutte polynomial and “q-state Potts uniqueness”
We establish for which weighted graphs H homomorphism functions from multigraphs
G to H are specializations of the Tutte polynomial of G, answering a question
of Freedman, Lov´asz and Schrijver.
We introduce a new property of graphs called “q-state Potts uniqueness” and relate
it to chromatic and Tutte uniqueness, and also to “chromatic–flow uniqueness”,
recently studied by Duan, Wu and Yu.Ministerio de Educación y Ciencia MTM2005-08441-C02-0
Distinguishing graphs by their left and right homomorphism profiles
We introduce a new property of graphs called ‘q-state Potts unique-ness’ and relate it to chromatic and Tutte
uniqueness, and also to ‘chromatic–flow uniqueness’, recently studied by Duan, Wu and Yu.
We establish for which edge-weighted graphs H homomor-phism functions from multigraphs G to H are
specializations of the Tutte polynomial of G, in particular answering a question of Freed-man, Lovász and
Schrijver. We also determine for which edge-weighted graphs H homomorphism functions from
multigraphs G to H are specializations of the ‘edge elimination polynomial’ of Averbouch, Godlin and
Makowsky and the ‘induced subgraph poly-nomial’ of Tittmann, Averbouch and Makowsky.
Unifying the study of these and related problems is the notion of the left and right homomorphism profiles
of a graph.Ministerio de Educación y Ciencia MTM2008-05866-C03-01Junta de Andalucía FQM- 0164Junta de Andalucía P06-FQM-0164
Chromatic equivalence classes of complete tripartite graphs
AbstractSome necessary conditions on a graph which has the same chromatic polynomial as the complete tripartite graph Km,n,r are developed. Using these, we obtain the chromatic equivalence classes for Km,n,n (where 1≤m≤n) and Km1,m2,m3 (where |mi−mj|≤3). In particular, it is shown that (i) Km,n,n (where 2≤m≤n) and (ii) Km1,m2,m3 (where |mi−mj|≤3, 2≤mi,i=1,2,3) are uniquely determined by their chromatic polynomials. The result (i), proved earlier by Liu et al. [R.Y. Liu, H.X. Zhao, C.Y. Ye, A complete solution to a conjecture on chromatic uniqueness of complete tripartite graphs, Discrete Math. 289 (2004) 175–179], answers a conjecture (raised in [G.L. Chia, B.H. Goh, K.M. Koh, The chromaticity of some families of complete tripartite graphs (In Honour of Prof. Roberto W. Frucht), Sci. Ser. A (1988) 27–37 (special issue)]) in the affirmative, while result (ii) extends a result of Zou [H.W. Zou, On the chromatic uniqueness of complete tripartite graphs Kn1,n2,n3 J. Systems Sci. Math. Sci. 20 (2000) 181–186]
Simultaneous Amplitude and Phase Measurement for Periodic Optical Signals Using Time-Resolved Optical Filtering
Time-resolved optical filtering (TROF) measures the spectrogram or sonogram
by a fast photodiode followed a tunable narrowband optical filter. For periodic
signal and to match the sonogram, numerical TROF algorithm is used to find the
original complex electric field or equivalently both the amplitude and phase.
For phase-modulated optical signals, the TROF algorithm is initiated using the
craters and ridges of the sonogram.Comment: 10 pages, 5 figure
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