Uniquely pairable graphs

AbstractThe concept of a k-pairable graph was introduced by Z. Chen [On k-pairable graphs, Discrete Mathematics 287 (2004), 11–15] as an extension of hypercubes and graphs with an antipodal isomorphism. In the present paper we generalize further this concept of a k-pairable graph to the concept of a semi-pairable graph. We prove that a graph is semi-pairable if and only if its prime factor decomposition contains a semi-pairable prime factor or some repeated prime factors. We also introduce a special class of k-pairable graphs which are called uniquely k-pairable graphs. We show that a graph is uniquely pairable if and only if its prime factor decomposition has at least one pairable prime factor, each prime factor is either uniquely pairable or not semi-pairable, and all prime factors which are not semi-pairable are pairwise non-isomorphic. As a corollary we give a characterization of uniquely pairable Cartesian product graphs

Outerplane bipartite graphs with isomorphic resonance graphs

We present novel results related to isomorphic resonance graphs of 2-connected outerplane bipartite graphs. As the main result, we provide a structure characterization for 2-connected outerplane bipartite graphs with isomorphic resonance graphs. Moreover, two additional characterizations are expressed in terms of resonance digraphs and via local structures of inner duals of 2-connected outerplane bipartite graphs, respectively

Resonance graphs of plane bipartite graphs as daisy cubes

We characterize all plane bipartite graphs whose resonance graphs are daisy cubes and therefore generalize related results on resonance graphs of benzenoid graphs, catacondensed even ring systems, as well as 2-connected outerplane bipartite graphs. Firstly, we prove that if $G$ is a plane elementary bipartite graph other than $K_2$, then the resonance graph $R(G)$ is a daisy cube if and only if the Fries number of $G$ equals the number of finite faces of $G$, which in turn is equivalent to $G$ being homeomorphically peripheral color alternating. Next, we extend the above characterization from plane elementary bipartite graphs to all plane bipartite graphs and show that the resonance graph of a plane bipartite graph $G$ is a daisy cube if and only if $G$ is weakly elementary bipartite and every elementary component of $G$ other than $K_2$ is homeomorphically peripheral color alternating. Along the way, we prove that a Cartesian product graph is a daisy cube if and only if all of its nontrivial factors are daisy cubes

Style-Label-Free: Cross-Speaker Style Transfer by Quantized VAE and Speaker-wise Normalization in Speech Synthesis

Cross-speaker style transfer in speech synthesis aims at transferring a style from source speaker to synthesised speech of a target speaker's timbre. Most previous approaches rely on data with style labels, but manually-annotated labels are expensive and not always reliable. In response to this problem, we propose Style-Label-Free, a cross-speaker style transfer method, which can realize the style transfer from source speaker to target speaker without style labels. Firstly, a reference encoder structure based on quantized variational autoencoder (Q-VAE) and style bottleneck is designed to extract discrete style representations. Secondly, a speaker-wise batch normalization layer is proposed to reduce the source speaker leakage. In order to improve the style extraction ability of the reference encoder, a style invariant and contrastive data augmentation method is proposed. Experimental results show that the method outperforms the baseline. We provide a website with audio samples.Comment: Published to ISCSLP 202

Improving Prosody for Cross-Speaker Style Transfer by Semi-Supervised Style Extractor and Hierarchical Modeling in Speech Synthesis

Cross-speaker style transfer in speech synthesis aims at transferring a style from source speaker to synthesized speech of a target speaker's timbre. In most previous methods, the synthesized fine-grained prosody features often represent the source speaker's average style, similar to the one-to-many problem(i.e., multiple prosody variations correspond to the same text). In response to this problem, a strength-controlled semi-supervised style extractor is proposed to disentangle the style from content and timbre, improving the representation and interpretability of the global style embedding, which can alleviate the one-to-many mapping and data imbalance problems in prosody prediction. A hierarchical prosody predictor is proposed to improve prosody modeling. We find that better style transfer can be achieved by using the source speaker's prosody features that are easily predicted. Additionally, a speaker-transfer-wise cycle consistency loss is proposed to assist the model in learning unseen style-timbre combinations during the training phase. Experimental results show that the method outperforms the baseline. We provide a website with audio samples.Comment: Accepted by ICASSP202

Forcing faces in plane bipartite graphs

AbstractLet Ω denote the class of connected plane bipartite graphs with no pendant edges. A finite face s of a graph G∈Ω is said to be a forcing face of G if the subgraph of G obtained by deleting all vertices of s together with their incident edges has exactly one perfect matching. This is a natural generalization of the concept of forcing hexagons in a hexagonal system introduced in Che and Chen [Forcing hexagons in hexagonal systems, MATCH Commun. Math. Comput. Chem. 56 (3) (2006) 649–668]. We prove that any connected plane bipartite graph with a forcing face is elementary. We also show that for any integers n and k with n⩾4 and n⩾k⩾0, there exists a plane elementary bipartite graph such that exactly k of the n finite faces of G are forcing. We then give a shorter proof for a recent result that a connected cubic plane bipartite graph G has at least two disjoint M-resonant faces for any perfect matching M of G, which is a main theorem in the paper [S. Bau, M.A. Henning, Matching transformation graphs of cubic bipartite plane graphs, Discrete Math. 262 (2003) 27–36]. As a corollary, any connected cubic plane bipartite graph has no forcing faces. Using the tool of Z-transformation graphs developed by Zhang et al. [Z-transformation graphs of perfect matchings of hexagonal systems, Discrete Math. 72 (1988) 405–415; Plane elementary bipartite graphs, Discrete Appl. Math. 105 (2000) 291–311], we characterize the plane elementary bipartite graphs whose finite faces are all forcing. We also obtain a necessary and sufficient condition for a finite face in a plane elementary bipartite graph to be forcing, which enables us to investigate the relationship between the existence of a forcing edge and the existence of a forcing face in a plane elementary bipartite graph, and find out that the former implies the latter but not vice versa. Moreover, we characterize the plane bipartite graphs that can be turned to have all finite faces forcing by subdivisions